I am returning to this conversation, after a rather lengthy email discussion with a gentleman who contacted me privately in response to my earlier remark.
The bottom line is: When it comes to the name that is spelled Mem-Yud-Chaf-Lamed, it's a matter of transcription and pronunciation.
1. In the Bible, King Saul had a daughter who later married King David. Her name is pronounced Mee-chal. The "CHAL" part is pronounced exactly the same as the "CHAL" at the beginning of the word "Challah". When this name is transcribed into English, it is spelled "Michal", with an 'a'. Many women -- especially in Israel -- have this name, and you can find some of the more well-known among them on the Internet, by googling with this exact spelling. (Seeking this name will also bring up a number of men who have "Michal" as a secular name, but this discussion is about Hebrew names, not Polish or other secular names).
2. There is a man's Yiddish name, often found in conjunction with the name Yechiel, that is pronounced Mi-chel. It rhymes with the Yiddish word tichel, a woman's small head covering. (Note that the 'ch' in all of these words is pronounced like the 'ch' in Chanukah, not like the ch in chair). The pronunciation might be made clearer by dropping the second vowel entirely, and writing it as Mich'l. Using the letter 'a' in the transcription of this name is misleading in both gender and pronunciation, and led me to my original comment.
I hope that this explains my original remark, and also hope to express myself more clearly in the future, should similar transcription ambiguities come up.
Brooklyn, New York, USA