Where does the male name מיכל (as in יחיאל מיכל) come from? Is it a diminutive/corruption/translation/elision of מיכאל, derived therefrom in some other way, or simply a false cognate?
In Igros Moshe Orach Chaim 5:10:2 Reb Moshe ZaTzaL writes that Michel is a Kinui (nickname) for Yechiel.
לפי תלמוד בבלי מסכת עירובין צו. מיכל בת שאול הניחה תפלין. האר"י מסביר זאת בכך שהייתה לה נשמה מעלמא דדכורא = נשמה מעולם הזכרים.
Maybe that is how the name became a male name?
Michel (emphasis on the first syllable) is a German form of Michael (says Wikipedia)
Aruch Hashulchan, Even Haezer 129, writes (in my own loose translation with uncertain translations marked with question marks in brackets [thus?]):
[We spell the name] "יחיאל". And some are nicknamed "מיכל", so we write [in a get] "יחיאל, who's nicknamed מיכל". Even though מיכל is a [non-nick name?], like "מיכל בת שאול" and like "מיכל מים", still and all, this name is based on a different understanding: Earlier, they'd call יחיאל "חיאל" for short; this [evolved?] into calling him "איחל", which [evolved?] into calling him "מיכל". And don't say that we should therefore write "מיחל", with a ches, as I've already brought the words of the Rama that it's better to write with a chaf than with a ches [a foreign name, "because there are places that read a ches like a he and there'll be a change in the name"], and that's how everyone practices already. However, in any event, since this isn't from the name "מיכל" which is in Tanach, we write "who's nicknamed" and not "who's called".
Sorry that I don't have a written source for this, however, I have heard this from several Lubavitchers, including the Rosh Yeshiva of the Tzemach Tzedek Yeshiva in Jerusalem. Essentially the Admur of Lubavitch, in one of his sichot made a statement that the alef may be corruption of the name, and thus it should be pronounced as if the alef were not there. I have met at one Lubavitcher that was named Michal(minus the alef) on account of that.