She really wouldn't have, but it can cause delays while they establish she's definitely the mother.
The very simple workaround is you stick an official copy of the birth certificate inside the child's passport.
I know all this because my missus has no truck with marriage or double barreled...
I once had a girlfriend with a double barreled surname. The funny/tragic part was that in a cringing Hyacinth Bucket way her dad had amalgamated his middle and last name in an attempt to boost his social standing.
The banging your head on the wall part was that this gave the family the...