I found a baptismal record (Church of England, 1765) which was transcribed (I believe in the 1940s) as given names "John Case" and his parents were unmarried (neither with surname Case). I noticed that for most illegitimate children in the same set of records, baptised by the same clergy, "Case" was added after the child's given name(s). My first though was that the original parish document (which I haven't seen) might have used "Base" as a short form of "Base born", but the notation is consistently transcribed over several pages and years. Also, at least one record where the parents were married Case was added and another where the mother's surname was Case. Any ideas?
ETA: Looks like "Case" was a transcription error of "Base". I found several examples in other parish records were "base" and "base born" look like "Case" and "Case born". when the B is in lowercase it can look like an uppercase C. Especially obvious when comparing two records on the same page in the Wiltshire, England, Church of England Baptisms, Marriages and Burials, 1538-1812:
* Mary Base Born, bap. 26 Mar 1723, of Frances Sommerset
* John Case Born, bap. 31 Mar 1723, of Anne Robinson