Baby last name

my bd wanna get mad bc I don’t want him to sign my son bc for one once I found out I had cut him off (bc I told him not to do it!!) and already had came up with his name now we have reconnected and he insists on signing it and I’m like noooo bc I already have his name and I told you not to do it anyways so no. How do you get to have a day so when I get to have a day in me getting pregnant? We’re not married and will never be and I don’t want my child carrying his last name