This app was mentioned in 1 comment, with an average of 1.00 upvote
AI Factory was the first one I played. I don't play it anymore.
This one is a port of GNUBG and is pretty good.
XG also has a mobile version and is very good, but there are some limitations in the free version, e.g., nothing more than 3pt match.
I know Backgammon NJ is popular, but I've never played it.