i live in California to. and have the same exact question
Obviously you should consult an attorney but child support is about paternity, not the last name. I know my step sister receives child support but baby has her last name, not the dad's.
Did you randomly meet this man or do you have sources that could possibly be solved by hiring a private investigator to check phone records Internet records the place you met him security footage any known relatives acquaintances or friends take notes of where when any one with u or saw u the night you conceived then afterwards look up online free attorney advice for family law in your state. Good luck
And your right you can literally put any name on the birth certificate but you have to establish paternity