Two Avimelechs?
Regarding Avimelech in Sefer Shoftim:
Q. Is this Avimelech Jewish and is he the same Avimelech that Avraham dealt with?
A. Thanks for your question, which was forwarded to my attention. The Avimelech discussed here was a Jewish leader and a different person from the Avimelech that Avraham knew. This Avimelech was the son of Gidon, the judge who preceded him.
Q. How can Avimelech be a Jewish name and non-Jewish name?
A. It's not outside the realm of possibility. After all, "Ron" is a name in English (short for Ronald) and in Hebrew (joyful song), as is Noah (a boy's name from the Hebrew "Noach") and Noa (a girl's name, meaning motion or movement). [After writing this, an even better example occurred to me: the Hebrew boy's name Elisha and the English girl's name Alicia. There are still others, like Eli/Elly, etc.] And it's not only with Hebrew that this might happen; consider the surname "Lee" in both English and Chinese.
But that's probably not the case here. First of all, "Avimelech" wasn't his given name, it was his title, like "Pharaoh" is how the Torah refers to all the Egyptian monarchs. (See Rashi on Tehillim 34:1, regarding yet another Avimelech.) Additionally, it's the Hebrew translation of his title. It's like we would refer to Claudia Sheinbaum as "the president" of Mexico, rather than "la presidenta" of Mexico.
As an aside, the original Avimelech's native language was Aramaic, so his title likely was something more like אבא מלכא (Abamalka), which isn't far off from the Hebrew (although it should be noted that Onkelos doesn't "reverse-engineer" the name back into Aramaic, so this is just a guess on my part).
I hope this helps!
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