do I have to change my daughters last name to my exes if she has my last name but I don't want too
If it's already on the birth certificate as your last name you don't have to change it that's her name now.
No you dont. Your baby can have whatever name you choose. Hypothetically speaking you can name your baby Chair On-a Moon and they can't do anything about it
Her name is her name now. Did you both sign the birth certificate?
Not at all