in 1811 she would proabably have been baptised as X illegitimate d/o AB & CD assuming the mother had divulged the father's name (as most such births were it seems courtship failures the mother (and I presume many around her) would have a good idea of the father's name though there are some cases on record where the putative father denies paternity.

by 1900 civil registration had started and that required notification and it would appear the manx had moved closer to the English norm of stimatising the mother (read a couple of T E Brown's poems on this topic) and the child was more likely to get the mother's name (the manx law that legitimacy was given if marriage occured within 2 years was repealed in 1929)