The island of Ustica was known, albeit imperfectly, in the ancient world, and the sources sometimes differ slightly...
Ancient Ustica in literature
The ancient sources about Ustica are Ptolemy (100-175 AD), Diodorus (who lived in the 1st century BC), Pomponius Mela (who wrote around AD 43) and Pliny the Elder (23-79 AD). Pomponius Mela wrote:
“[...] “nearer Italy, Galata and those seven they call the isles of Aeolus [the Lipari islands], Osteodes [Ustica], Lipara [Lipari], Heraclea [Alidudi], Dydima [Salina], Phoenicusa [Filicudi], and the two like Aetna, Hiera [Vulcano] and Strongyle [Stromboli], which burns with uninterrupted flame” .
Pliny, on the contrary, believed that “Osteodes” and “Ustica” were two different islands. In fact, he wrote:
"[…] The islands toward Africa are Malta, 87 miles from Camerina, from Lilibeo one hundred thirteen. Cosira, Hieronneso, Cene, Galata, Lopadusa, which some call Egusa; Bucinna and ‘Osteodes’ seventy five miles from Solonte and ‘Ustica’ in front of Paropini [Termini Imerese]” .
History of Ustica in ancient times
Moving on to historical facts about Ustica, we can say that its entire history is related to the small local population. According to studies, the island had a population of some significance in the late-Roman and Byzantine times, but in later centuries and in the Middle Ages it was virtually depopulated.
In fact, according to Fernando Maurici, the transition from Late Antiquity to the Middle Ages, and the advent of Arab piracy in the Mediterranean, began a crisis that affected the presence of inhabitants on the island for many centuries. The locals were always victims of piracy, with the risk of ending up in slavery or being killed, so the island was gradually almost entirely depopulated.
Ferdinando Maurici said that:
"the almost total abandonment and sporadic attendance by sailors and pirates characterize the medieval history of Ustica, such as Lampedusa and Linosa, small islands, completely let down and poor in resources." 
In the 13th century the monastery of “Santa Maria de Ustica” was created here, but it declined quickly and disappeared within the first half of the 14th century. Therefore Ustica was visited only occasionally, essentially becoming a dangerous hiding place for pirates and corsairs.
18th century repopulation of Ustica
Ustica started to have a stable population only in the late 18th century, and in this period there was an attempt to improve the safety conditions of the inhabitants.
In 1761 it was re-populated, precisely to avoid it was only being used as a haven for pirates, by transferring to it some of the inhabitants of Lipari, but after an initial defeat in 1762, the pirates retook the island, catching many residents although some managed to evade capture by hiding in the caves of the island .
The issue was finally resolved in 1763 when a contingent of soldiers and workers was sent from Palermo to Ustica, who began the construction of fortifications on the hill of the “Falconiera”, and two towers on opposite sides of the coast, that is above the creek of St. Maria and on that of “Punta Spalmatore.” In the same year 85 families of farmers and fishermen reached here from the Aeolian Islands, as well as a few artisans from Palermo and Trapani, to give a total population of 400 people.
During the same period the layout of the island was defined, with a central church dedicated to St. Ferdinand in 1765.
Origins of the name Ustica - load of old bones?
The etymological problem with Ustica is both simple and difficult. It's simple, if we refer to the etymology of the Latin term of the isle, which the Romans called "Ustica", from "Ustum" ("burned"), because of its volcanic nature.
Otherwise it is difficult to determine whether instead we refer to the Greek word, “Osteodes” (“ossuary”), with reference to a legend handed down by Diodorus (V. 11), who is also the only ancient source, and perhaps based on Timaeus (350-260BC).
According to this legend the word “ossuary” is related to the fact that the Carthaginians left a lot of mercenaries who had rebelled against Carthage here to starve. The “bones”, according to Diodorus, were those of about 6000 mercenaries left to starve on the island.
We note that this etymology, and the story of mercenaries, is quite uncritically repeated in most of the studies concerning the ancient history of Ustica. However, things are a bit more complicated. Garret G. Fagan and Matthew Trundle, talking about the problem of the traditional "cruelty" against the enemies of the Carthaginians, do not have faith in this Greek etymology and consider it:
"[...] the dubious aetiology of the ‘bony’ island (‘Osteodes’) [...]" .
Even more specific was the essay by G. Amiotti, who through an extremely tight analysis of the sources, denies that the Greek etymology "Osteodes" ("ossuary") has any foundation, and she thinks of a Phoenician etymology, because, according to K. Ziegler  Osteodes is not a Greek name:"
[...] Whatever the precise time of the mercenaries revolt, it is improbable that the island received its name "after" the incident narrated by Diodorus, V, 11. "Ustica" certainly has a popular etymology: the name is not Greek, but it could be a Phoenician Hellenized name.
In fact, the island belonged to the Carthaginian sphere of influence and it was not included in the shipping lanes of the Greeks. It’s significant, moreover, that Diodorus does not mention Ustica for geographical reasons, but in relation to an episode of the war of the Carthaginians against the Syracusans, probably taking this information from Timaeus [...]" .
It must be clear, however, that G. Amiotti so does not deny the fact that the Greek etymology of Ustica is "ossuary", but just that it is referring to the episode of the revolt of the mercenaries against Carthage.
Since the Phoenicians colonized the island long before the Greeks, it is a bit hard to believe that they had not given a name to the island. S. Vassallo writes:
"[...] In the Middle Bronze Age, too, the distribution is different with examples from the Aeolian Islands (at Panarea ) ... and in the prehistoric village of Ustica, with five specimens dated to the period between the Middle and Late Bronze Age [...]" .
Some interpretation of the Phoenician origins of Ustica was attempted in the 19th century, but that did not enjoy too much credit and the idea was abandoned. However, Peter Calcara wrote:
"[...] Seeing this island very low, Bochiard (Samuel Bochart) believed that the etymology of Ustica came from the Phoenician language, and meant 'flattish', or 'curved'. Others, more wisely, derive it from Latin, meaning 'scorched earth' for its volcanic origin [...]" .
More recently, we note that "according to Samuel Bochart, Ustica is a Phoenician word meaning 'level and low place”, or "[Ustica] is a word that means "low" and "bending" because it is flat for the most part". Then he points out that Horace [65-27 BC] ("Odes", I, 17) gave a similar description of the island, calling it "Ustica cubantis" (Ustica low ) . About Horace, however, we observe that he was not referring to the island of Ustica, but a hill of Sabina, known as "Ustica", very close to his villa.
In summary, as Pietro Calcara said, there is no doubt about the Latin etymology, accepted by all scholars - the question concerns only the Greek name and its etymology.
Perhaps the Greeks actually found many human bones on the island, calling it for this reason "ossuary", but it is probable that the tradition concerning the extermination of the mercenaries is wrong. Very likely the presence of many bones is best explained by the fact that on the island there are ancient Phoenician necropolis, a fact widely known to contemporary critics.
We can conclude that there are two etymologies for Ustica, and both exact. The Greek version refers to the presence of many bones (but not for the reasons given by Diodorus) and the Latin version, which seems to refer to volcanic island and its aridity.
... However, this “double etymology” is not at all convincing. The Latins were strongly "Graecizing" and usually Latinized Greek terms. We can even say that to "graecize" for the Roman educated class was a real "mania" and often criticized by members of the pure Latin tradition. Therefore, we do not understand why, precisely in relation to "Ustica", this did not happen.
In short, in the case of Ustica there would be an incomprehensible "discontinuity" between the Greek and the Latin term. M. Congedo emphasized that:
"the Greek form ‘Osteodes’, and the more simple "Ostodis" (with the loss of "e") did not survive, driven by the Latin form 'Ustica'" .
However, as we said, it is not convincing. Meanwhile, we observe that the "vulgar" form “Ostodis” is very close to the Latin term "Ustica", and it probably should be interpreted in a different way than the tradition. The Latin verb "uro", "urere" was also used in the sense of "burn" (the dead), and therefore, even in a metaphorical sense, it recalls the Greek concept of "bones" (of the dead).
If the verb "burn" refers to the cremation and not to the volcanic nature of Ustica, the two etymologies are much closer and corresponding than what we normally believe, and in this way, at a conceptual level, it has apparently bridged the gap between "Osteodes" and "Ustum”.
In fact the Latin language, for "burn the dead," uses the word "cremare" [English “cremate”] but also "urere"; "cremate a dead body," according to Cicero, was in fact "mortuum urere hominem." In conclusion with "Ustum" the Latins meant metaphorically the "dead", and "Osteodes" refers conceptually to the "dead".
It would also be very interesting to know the ancient Phoenician name of the island, to see if the Greek name "Osteodes" corresponded in some way to the Phoenician term. Unfortunately we do not have specific studies about the topic. The only thing we can say is that some attempt at interpretation was made (but with poor results) in relation to the town of "Utica", a name that is like “Ustica”.
M'Hamed Hassine Fantar noted however, that the Phoenician names beginning with "U" perhaps refer to the concept of "son of", but without the necessary details, so that the Phoenician name of “Utica”-“Ustica” remains a mystery:
"[...] The name 'Utica' continues to interrogate the experts and to excite controversies (...) [however] the initial 'U' of Utica is in many place names of Libyan origin, such as 'Usalis', 'Uthina', 'Uchi', 'Uchres', 'Usappa'. The Utica place-name (...) should be attributed to this series of names beginning with the letter 'U', which in Libya could mean ‘son of’ […]” .
See also the Ustica travel guide.
1. See Pomponii Melae, “De Chorographia”, Libri Tres, Berolini, 1867: 60
2. See C. Plinius Secundus, “Naturalis Historia”, edidit L. Ian , Teubner, Stuttgart und Leipzig, 1996: 268
3. See Garret G. Fagan, Matthew Trundle, "New Perspectives on Ancient Warfare," Brill, 2010: 284
4. RE, 18, 1942, "Osteodes" columns from 1646 to 1647
5. See Gabriella Amiotti, “Ustica, L'isola solitaria” [“Ustica, the solitary island”], in G. Vanotti-C. Perassi, “In Limine. Ricerche su marginalità e periferie nel mondo antico” [“In Limine. Research on margins and periphery in the ancient world”], 2004: 307
6. See S. Vassallo, "The Stone Casting Moulds from Colle Madore," in R. Gocha Tsetskhladze, "Ancient West & East, Brill, 2004, Vol. 3: 33-35
7. See Pietro Calcara, “Descrizione dell'isola di Ustica” ["Description of the island of Ustica”], Palermo, 1842 , Excerpt from the “Giornale Letterario” ["Literary Journal"], n. 229: 63 footnote 2
8. See L. Clerici, “Scrittori italiani di viaggio” ["Italian travel writers "], Mondadori , 2008: 76
9. See M. Congedo, “La viabilità della Sicilia in età romana” ["The Roads of Sicily in Roman times "], 2004: 54
10. M'Hamed Hassine Fanta, “I Fenici”, in “Storia del Mediterraneo nell'Antichità” ["The Phoenicians", in "History of the Mediterranean in Antiquity”], edited by M. Guidetti, Milan, Jaka Book: 40
11. Ferdinando Maurici (“Per la storia delle isole minori della Sicilia” in “ Acta historica et archaeologica medievalia”, 2001: 193, 202
12. See S. Bono, “Lumi e Corsari. L'Europa e il Mahgreb nel XVIII secolo” ["Enlightenment and Corsairs.The Europe and Maghreb in the eighteenth century"], Perugia, Morlacchi, 2005: 27