My paternal 3rd great grandfather, Samuel Abraham(s) was born about 1806 according to the England 1841 Census. I know I should either add or subtract 5 to that as they were know to round the number.
When Samuel and Mary Cockayne married there were no parents listed. I contacted the church and verified that the parents were not listed. Samuel died, I believe, 1849 in Nantwich, England and it was listed that his father was Marcus. So if his father was Marcus, he did not follow the pattern which all families followed during that time by naming his first son the name of his father. His children, that I know of, are as follows: Lewis abt. 1831-1891, Samuel 1834-1836, Caroline abt. 1836-?, Charlotte abt. 1837-1902, George H. 1838-1840, Harriet abt. 1840, Mark Henry abt. 1842-? and Eliza abt. 1846-?.
Our name was change to Brahams. Also, we are not Jewish. Abrahams i commonly a Jewish name and there was a story told that the Abrahams were Jewish until one of the boys married a Christian and they were cast away from the family. Could that have been Samuel and is that why I can't find anything? So those are my things about Samuel.
Jenn - Naming patterns were not followed by all families as you stated in your query. Some families followed them but many did not. And I note that there was a child named Mark Henry - Mark being a shortened form for Marcus.
A Charlotte and Catherine Abraham of the right ages can be found in the Hebrew Girls Boarding School, Palestine Place in 1851. They are in the census for that year for Tower Hamlet, St. John's, Bethnal Green, Middlesex England. So it seems there may be some truth to your family lore.
Also you might want to make note of the fact that some of the children are listed twice in the 1841 census - once with their parents Samuel and Mary, but also in Manchester with Mary Cockayne age 63 with daughters Eliza and Fanny as well as the Abraham children Lewis, Caroline and Charlotte.
A quick search for a few of the children turned up Harriet's baptism - as Harriet Ellen Abrahams to Samuel and Mary on 29 Aug 1849 in Manchester. Her birth date is given as 18 Aug 1839 and Samuel is noted as a Commercial Traveller. He is not recorded as being deceased at that time although another record indicates he was buried 30 Jul 1849 in Nantwich. A second child named Eliza Cockayne was baptised the same day to Samuel and Mary (whose name is given as Mary Ann). Her birth was 1845.
If I were you I would search each of the children thoroughly - see who they married, when and where they died. Look for burial records, obituaries, church death records to gain more information on the family.