By the time i was in my 30's due to how many people were serially monogamous, Mom's and children not having same name was becoming common. Took first husband's name and kept till civil cermony marriage to #3.
Second, a common law husband, left when i was 6 months pregnant with daughter. (He at least paid child support until she was 3 months old and visited her some while we were in same state.) So i put my maiden name on her birth certificate.
So for several years we were three last name household. When divorcing #3 i lucked out: We were in Wyoming, where this a question on divorce papers about retaining married name or returning to maiden name.
By that time my sons were grown, daughter a teen, and now because i'd given her a family first name (she's 5th generation in matriarchial line with that first name) we had same name except for middle. Which makes putting our middle initials on forms and documents crucial. At medical providers they usually use date of birth along with name as identifier so that's easier.
But we've thrown more than one telephone solicitor of their script by asking 'Which one?' when they ask for us by either first or both first and last name.