Just re-name the dog. This seriously isn't a big issue. If she's aware that you were going to name the baby that then shes probably rude and hinting that she doesn't like it. If she wasn't aware then I'm sure she will understand.

thats totally selfish of her

That's hella ****** up.

Nicknames my friend. Nicknames...

That's my name... I'm so glad it's a worthy dog name >:(

That's incredibly insensitive and inconsiderate

No reason you can't give it to your baby still.. But if it really upsets you that much try talking to your mom. If she refuses to rename the dog then tell her she wont be able to see her grandchild. Or (though I couldn't recomend this x-x) kidnap the dog and give her away to someone else.

My name is Olivia. That isn't a dog name either. Dogs remember names that have few syllables, and since Olivia has four, it will be hard that dog to remember the name, so try to name it something it will easily remember.

Who cares? The dog won't live long compared to your daughter anyways

Keep the nice name, OP. Your mom will get payback as your daughter grows up thinking the dog is really her's.