For the historical inhabitants of Troy, it depends what period you're talking about. For the Bronze Age city (Troy I to VI), we have no reason to imagine the inhabitants as Greek in any sense: we don't know what language they spoke -- Luvian is probably the best bet, but it isn't a sure thing -- but material culture is primarily Anatolian. After the end of the Bronze Age (Troy VII) there's some evidence of migration from Thrace.

There was a gap in the settlement of the site from ca. 950 BCE for around two hundred years. When it was resettled in the 700s (Troy VIII onwards), the colonisation was Greek, but there was a significant mixture of ethnicities in the people who were already in the region. Textual sources describe the main groups as Mysians, Phrygians, and Lelegians. For that reason Troy was not considered part of Aiolis, the string of Aeolic-speaking Greek colonies along the west coast of Anatolia south of Troy down to Smyrna (modern Izmir).

If it's the legendary Troy that you're interested in, then the most important part of the answer is that a fictional city can be said to have any ethnicity you like. It depends entirely on who's telling the legend. In Dictys of Crete and Quintus of Smyrna, for example, they're cast as some vague non-Greek ethnicity. In Homer, it's more complex: on the one hand, most named Trojans have Greek names, their gods are Greek, and the main civic cult is the classical-era cult of Ilian Athena; on the other hand, Priam's family living arrangements sound non-Greek (fifty sons by several women, all living in one house) and certain scenes cast the Trojans and their allies as a mix of several ethnicities. (This last bit sounds like a true-to-life reflection of Troy in the 7th century BCE, at the time the Iliad was composed.)