Hospital and baby registration

I’m 33 weeks rn and my baby daddy (my bf) he’s going to the navy bootcamp In 2 weeks and he. Calculated when he’ll be done with bootcamp and then going to school and it’s gonna be after she’s born. My bf won’t be there for her birth but she needs his last name to receive any benefits am I able to still give her his last name if he’s not gonna be there to sign the papers? His recruiter told him he can sign the birth certificate when he’s done with bootcamp. I’m not sure please help