Bender is a bending unit.
Bender was given the name Bender, same as Flexo was given his name.
Under the assumption that bending units are given names having to do with bending, are there other bending units also called Bender?
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There have not been any other bending units with the name "Bender" appearing in the series (not counting parallel Benders or time paradox duplicates). However, there have been two other named robots with the same appearance as Bender: Flexo and Billy West.
Also, Bender was just a particular model of bending unit: model #22. There have been other models of bending units, both male and female (such as Angleyne). Here are some other models from the bending competitions of the Robot Olympics: