I think the answer is
Riley
My prefix is called an island.
The island of Rye, or the state code for Rhode Island, USA (RI).
My infix is an island.
ile, sounds like isle
My suffix is not so windy.
ley, not so windy as in "using or expressed in many words that sound impressive but mean little", indeed, it is very short.
Or
lee, as in "protective shelter", more likely to be the intended answer to the clue :)
I made this puzzle.
Riley, the first to drop one of these types of riddles here..