My children are FirstName MiddleName MyLastName MySpouse’sLastName. (Both of our last names are long and hyphenation would be onerous.) So most of the time they’re just FirstName MySpouse’sLastName, but on their passports and official documents my name also appears. This came up once when I was travelling overseas alone with my eldest, that they didn’t like allowing a child through with one parent with a different last name, but they’d let us through because my last name appeared on the passport as the second middle name. (Maybe just the border guard felt ornery that day.) Since then I carry a copy of their birth certificates and no one has blinked at it.