MY LAST NAME OR HIS LAST NAME?

My partner is married to another woman pero matagal na po silang hiwalay bago pa po kami nagkakilala. Fyi, hindi po sila separated or annulled kasi malaki pong halaga ang magagastos para maprocess yun. May verbal agreement rin sila na hiwalay na sila though wala pong written agreement. may new partner narin po ang ex wife niya. Anyway, magkakababy na po kami soon. So ask ko lang po.. should I use his last name or my last name for our baby? Ano pong mga magiging problema in the future? No judgement please. Thank you.