I mean technically speaking they wouldn’t be able to be legally married but if we want to throw homophobia from the past into the garbage (where it belongs), I think they would hyphenate their names? That or not change their own names.
This is a side thing, but I headcanon Maxwell being his middle name, so his full name is William Maxwell Carter.
Idk what they’d put down for Wren’s last name though. They might argue about it lkfhsdlfkjsd