During the wide window, when Klaus and Poe are arguing about being adopted by captain sham. Poe said that soon he will be Klaus sham.Does that mean that they were (briefly) the Montgomery ,Anwhistle siblings for legal matters? even if they continue to refer to themselves as Baudelaire.
Technically, Montgomery and Josephine were both legal guardians, and not adoptive parents. There's some other differences, but the relevant part in this case is that the children wouldn't take their last names, but they would if Captain Sham actually adopted them.