I am I wrong for wanting to give my baby my last name?

A few weeks ago I had posted a video announcing my baby’s name. My partners mum seen the video and was not happy. Saying how it’s unfair that she was not going to have their last name and that babies usually take on the fathers last name. (Even though she gave him hers) She explained in a message to him making it all about her self that she was finding it very hard how my baby would take on my last name and not hers. I told her she was not going to change my mind and me and my partner had decided on our babies name long before she was conceived. She was making me feel like her surrogate. To add a bit of background context: (she convinced my partner that we should have a baby is it would “sort us right out” she couldn’t have anymore children of her own and always wanted a daughter) she sent multiple messages telling my partner one thing she asks is to make sure to get their name on the birth certificate. I didn’t see why she was so bothered unless there was a hidden agenda. She also set up a nursery in a spare bedroom and invited me and my partner to live with her when the baby arrives so she can “give us extra support” I refused as I don’t want to move away from my family. Since I told her I was not giving our baby their last name she became really vicious stating she “didnt want to be landed with my child” and accusing me of the baby not being my partners. Not once did anyone say she would be landed with my child. She then went to say she would take me to court because I said she wouldn’t be able to see her. I am I over thinking that she wants my baby? Or am I right?