This site says that
Taina is a Finnish short form of
Tatiana.
Have you asked your parents where they found the name? Since you are from the Caribbean, it's possible that your parents feminized Taino, the name of one of the most prominent Native American nations in the Caribbean Islands.
http://www.topuertorico.org/reference/taino.shtml
There are some other sites on the Web that say that Taino originally meant "good and noble people." This may be true, but I haven't yet found a site about the Taino language that confirms it.