The Mormons can’t be blamed for assuming that an illegitimate child would take its mother’s surname. With the Manx there is no way of knowing. Searchers will be best helped by indexing them under each name, with a symbol to indicate illegitimacy.
When searching Cumberland records at the Society of Genealogists I found that each marriage appeared three times in the index: under the groom’s name, under the bride’s maiden name, and under the bride’s married name. That is something to consider doing here. If the details immediately follow the indexed name, as in the IGI, it will be clear whether the bride’s name is a maiden or married name. If the indexed name is followed by a reference to look up, then again, a symbol can be used to indicate maiden or married.