Is your fiance your income tax dependent?

Yes, if she qualified as your dependent. Otherwise, no.

However she may use the money you paid to claim the tuition credit or deduction on her own return*. If she is the dependent of her parents, they may claim the money you paid. 

*A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit, on his/her own return, if he supports himself by working. He/she cannot be supporting himself on support fro other people, 529 plans or student loans & grants. He/she must have actually paid tuition, not had it paid by scholarships & grants.  It is usually best if the parent claims that credit. 

 

If this was a Married Filing Separately situation, where I paid my fiance's tuition, only she could claim the education expense credit, correct?

Not exactly. The education credit is not allowed to anyone who files  Married Filing Separately (MFS). But "fiances"  don't usually file MFS; they file Single. So,  If you paid her tuition, but she was not your dependent, and filed her own return, claiming herself; she could claim the education credit even though she didn't pay any tuition herself.

Ah I see, so since it was in "her name" she claims it.

Again, not exactly. It's not that the school registration or 1098-T is in her name; it's that the tuition credit goes with the student's exemption (dependency). If she claims herself, she gets the tuition credit. If somebody else claims her as a dependent (whether it be her parent or her fiance), that person gets the credit