is this rhyme known by any other name?
Yes, Black Paternoster
Matthew, Mark, Luke and John
Black Paternoster
matthew mark luke john bless the bed that i lay on It  is an English children's bedtime prayer and nursery rhyme. who composed it? UNANSWERABLE
wiki:434903
Matthew, Mark, Luke and John [SEP] Introduction
"Matthew, Mark, Luke and John", also known as the "Black Paternoster", is an English children's bedtime prayer and nursery rhyme. It has a Roud Folk Song Index number of 1704. It may have origins in ancient Babylonian prayers and was being used in a Christian version in late Medieval Germany. The earliest extant version in English can be traced to the mid-sixteenth century. It was mentioned by English Protestant writers as a "popish" or magical charm. It is related to other prayers, including a "Green" and "White Paternoster", which can be traced to late Medieval England and with which it is often confused.