I've never heard of this as a Maori name - and
Tiana doesn't mean "
Princess", either.
According to this site,
Tiana is a short form of
Christiana (follow the hyperlinks for details). Elsewhere I've seen it as a short form of
Tatiana - either is possible.
Tiahna is a variant spelling of
Tiana, along with Tian, Tiane, Tiahn,
Tianna, Tianne etc.
:-)