Name change/ Multiple passports

Wondering if anyone knows the answer to this, I hold dual citizenship (Mexico & US) but am wondering if a name change would require me to update my Mexican passport as well. I recently married and am changing my last name but not sure how updating Mexican documents go/if necessary.

My Mexican and U.S. Passport are linked to Global entry & I’d assume I’d need my name to match on both documentation. I’m more than willing to but don’t want to spend more if not needed and know maiden name is most common and easiest in Mexico.

Anyone have experience on this? Do I need to update my Mexican passport as well? Can I go through the online process with this ?