I think you are asking could she use an alias --
no ID required then . If in a big city in England
or having moved to somewhere new I think it
was very possible. In the IOM then with a
much smaller population & fewer newcomers it seems
probable the staff could identify inmates more easily.
A new mother would I believe have been pressured
to say where she lived / was in service/ which parish
she was from although not asked to swear a sacred oath as once would have happened at Church Court.