For years I couldn't trace the birth or baptism records of the children of a couple who I had the marriage of, and both wills of, so knew the names of many of their children. I suspected they may have been non conformists, but didn't do, what I now see was rather obvious - search JUST for the name of the ancestor with no parent's name put in

! I think whenever I looked for the baptism or birth records of the ancestor or her siblings, I was always putting in at least the father's first name. But on finding another will, which mentioned an unknown sibling with a much more unusual first name, that led me to the register of the New Broad Street Independent Meeting in London, under the leadership of John Guysse, minister, an independent and supporter of Calvinism
https://www.wikitree.com/wiki/Space:History_of_Nonconformists_in_London%2C_England_and_surrounding_counties#New_Broad_Street_Meeting_Househttps://www.google.co.uk/books/edition/The_History_and_Antiquities_of_Dissentin/wpIsAAAAYAAJ?hl=en&gbpv=1&pg=PA229&printsec=frontcoverAll the baptism records are grouped by family, all in the form
Mr. Cooke's Daughter Sarah Sept. 23. 1728 (Apothecary)
son John Oct. 20. 1729
Daughter Sarah Dec. 1. 1732So, unusually for the period, you do get a father's profession, but no name!