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".