Having trouble changing my name after marriage (posting here due to it involving latino culture)

My husband is latino and I learned it's common in his culture that they have 2 last names. He has his father's last name and then his mother's maiden name. I don't have to take his mother's maiden name from what I researched and also a bunch of Miami folks on reddit said so 😅 Supposedly I can just take his father's last name, which is what I want.

I was successful at the social security appointment and my social security card has just the one last name now (his father's) but at the DMV they wouldn't do it because our marriage certificate has his full name with the 2 last names and they said mine has to match.

She said I can show a life insurance policy that shows his name with just his father's last name (not an option) or i can have my passport with my new name and the passport will be used at the DMV in place of the marriage certificate.

But when I change my name on passport they will also go by the marriage certificate I assume?

This doesn't seem right. I dont have to take his second last name right? Our daughter's birth certificate is just the one last name.

Also on a lot of his accounts (bank accounts, our health insurance, etc) it only has his first name and 1 last name (the father's last name) so he has proof showing he goes by both.

I'm asking here in hopes someone had the same situation.

Thanks!