MoonSong
Rules-lawyering drama queen but not a munchkin
Most likely she was elected not by universal suffrage, but by a council of nobles. Like in most elective monarchies.This tangent about elections is relevant here because, whereas I could accept that her first name might actually be some sort of mystery or at least a very obscure fact if she was a royal with fourteen first names, raised in some sort of forbidden city and only revealed to the world when she adopted the regnal name Amidala, having her just be an elected politician named Padme Amidala who ran for the office of Queen a year or two earlier makes it feel like Qui-Gon and Obiwan did not actually read their mission brief at all.
As for the name thing, i think it is refuge in audacity. If you suspect the Queen is using a body double, you would probably suspect the handmaiden with the same name first, but you would also easily dismiss it because, it is too obvious for anybody to attempt.

