"What is this thing?"
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Princess is a title rarely used in the context of Metroid, although some princesses from other franchises have interacted with it in various ways, such as in Super Smash Bros. You may be looking for:
Samus Aran, who has the nickname "princess" in Metroid: Other M, but is not royal by blood or marriage.
Princess Peach
Princess Daisy
Princess Zelda
Lucina
Corrin (female version)
Princess Lana
The Legend of Zelda: Twilight Princess, one of the games that rewards Ship Bumper Stickers