If "chosen" means "in-law", and not specifically "father-in-law",
there's no need to assume that one person had three different names.
Reuel was priest of Midian when Moses arrived, and Moses married his
daughter, but Yeser was head of the family when Moses asked his
permission to return to Egypt. Yisro (a variant spelling of Yeser)
brought Moses' wife and children to him at Mount Sinai; by that time
he was priest of Midian. Hovav, (another) son of Reuel, stayed for a
while, and Moses asked him to guide the Jews in the desert, which he
apparently declined to do. On the other hand, it's perfectly possible
that Reuel was also called Yeser/Yisro; we know of several people who
had two names, including Sarah/Yiscah, Yaakov/Yisroel, Esau's wives,
and many of Jacob's grandchildren.
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