I'm not religious and would not be a happy camper if the ex tried to get our daughter baptised.
That said, if he was already raising her as a Christian anyway, sending her to a Christian school and whatnot, then my issue would be with THAT and not the baptism. Baptism on its own is less against what I want for my child than religious teachings in childhood. So it seems kinda pointless to even debate it - if she can teach her kid to follow Christianity, and the Dad is okay with that... what's the big deal with baptism?
I don't get the hyphenated name thing though. If the kid is happy enough to have their name changed, then why can't it be done?