It definitely feels made-up to me. Which isn't necessarily a bad thing in my books. But what I dislike about it is the "ay". For me, that lumps is in with the ayden,
Jayden,
Cayden,
Hayden,
Brayden, Grayden, Vayden crowd. Plus the
Hayley,
Kayley, Bayley, Brayley crowd. And then there's the Shaylynn, Braylynn,
Kaylynn crowd.
Basically, Baya just gets lost in the crowd.