Michaelmas (n.)

masc. proper name, also the name of an archangel, from Late Latin Michael (source of French Michel, Spanish Miguel), from Greek Mikhael, from Hebrew Mikha-el, literally "Who is like God?" The modern form of the name was a learned form in Middle English, where the common form was Michel (also Mihhal, Mighel, etc.), from Old French. The surname Mitchell might be from the old pronunciation of Michael or in some cases it might be from Old English mycel "big."

"eucharistic service," Middle English messe, masse, from Old English mæsse, from Vulgar Latin *messa "eucharistic service," literally "dismissal," from Late Latin missa "dismissal," fem. past participle of mittere "to let go, send" (see mission).

Probably so called from the concluding words of the service, Ite, missa est, "Go, (the prayer) has been sent," or "Go, it is the dismissal." The Latin word sometimes was glossed in Old English as sendnes "send-ness." Meaning "musical setting of certain parts of the Catholic (or Anglican) liturgy" is by 1590s.