Well, I checked, and indeed it is easy to find numerous pages saying that
Tia is a name of Greek origin meaning "princess". The same is said about
Tiana (of which
Tia could be a short name), with the occasional page thrown in that says
Tiana means princess in Gaelic instead of Greek.
What I could not find however is any confirmation that this info is true and not only endlessly copied from one website to another.
I personally doubt the "princess" meaning.