When, historically, do you need the name for? If the Spanish founded the first settlements there, they would have a name for it, but there's no telling whether subsequent nations would have respected that name, or given it a new name. Even if they simply used the same name, it would be a loanword, and would thus change to conform to the phonology of those languages, and over time would evolve with the language. However, if they didn't use the same name, there could easily be five or six names for the island. But, the likelihood is that if you get as far as the late 19th Century, one or two of those names would be dominant, depending on who represented the place in international diplomacy. Really, from what others have said, and from this, you should get the idea that we (and possibly you) need more information about the place before you can give it a realistic name.

I have an excellent article I downloaded years ago that seems to have gone offline.

Name Lang.doc

It is meant for creating a basic constructed language for the purposes of naming places and people in a fabricated setting. However I can see how you could use it perfectly adequately for naming made up place in the real world. Just ignore the first part of the article about making the language, and go on to the second part about using it to make your names. Use Spanish, Middle/Early Modern English, French, Dutch, (only English has changed significantly in that time period) or whatever other language you find relevant in place of the naming language. It contains a basic description of sound change in proper names, but you can apply the principles to a place name too.