I think someone got it spot on early in the replies......its YOUR child not your MIL. She has name her child/ren!
I'm sorry but I do not get along with my MIL so I always wonder why someone would do something to please them! also do you have family? Mother etc? Cause what makes her think she has all the say then, what if they have a traditonal name?

At the end of the day this is your child & you are the one who has to be happy with the name not your MIL. In regards to the father of the child then YES he should be happy with the name also, so perhaps you can come up with something together....just don't tell anyone else what.