There is a rabbi in the Talmud referred to as רבה בר בר חנה. Why is he called that way? It says that Rabba was the grandson of Chana.
Who was Chana? Was it(?) a woman? Why wasn't he called after his father or grandfather?
Who was his father?
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I have a book about the personalities of the zugos - geonim era. It quotes an opinion that suggests that Rabbah bar bar Channa is in fact the son of Rabbah bar Channa, whom we find elsewhere in older manuscripts (since many printers later confused him with Rabbah bar bar Channa), who in turn is the son of Channa, brother to R' Chiya. According to this, it suggests that Rabbah bar bar Channa is called by his grandfather's name, since he had the same name as his father, which apparently the Talmud felt would be confusing.
Also, Channa would consequently be male, and although I'm not sure of the correct vowelization, the book I quoted above feels that his name should be spelled "חנא" (though I don't see that this is justified).
Chono was his grandfather (not Chana). The reason his father's name was unknown is due to Gezeiras HaShemad in those times.
Could it be simply that his father's name was actually "Bar Chana"? There are quite a lot of figures mentioned in the Gemara who are called "Ben/Bar X," and it doesn't seem like all of those are patronymics or locatives.
(For Biblical equivalents, consider "Ben Chanan" and "Ben Zoches" in I Chron. 4:20. A later example of a personal name formed in this way is Ben Tzion.)
it explains in the artscroll about his name in BabaBasra, in the agada that deals with Bar Chana's adventures. I don't remember why they called him Rabbi Bar Bar Chana but his real name is Abaye, but he is not the Abaye that is commonly refered to in the gemera. Mabye they called him Rabbi Bar Bar Chana so he wouldn't get confused with Abaye?