s2021~ women/people come up to you & ask you ‘what’s your married name?’ as opposed to just ‘what’s your name?’? … that’s peculiar. it would make more sense if they asked you ‘what’s your family (maiden) name?’ if they see you’re wearing a sheitel.
if they have to ask your name, they probably don’t know you very well to begin with… so what does it matter what last name you give them?
good idea to stay away from untruths.