A general comment about name changes - ppl did often include the name of an influential relative in their children's names eg Elizabeth Armstrong Haggerston (a relative of mine) Armstrong was a maternal family name which the family wanted to recognize or perhaps there was a wealthy maternal relative who might be influenced by the use of the name eg a maiden aunt.
Sometimes this was reversed and the family name from the maternal line becomes the name used in the paternal line, for a variety of reasons - so the name is not lost, to make someone an heir where there are no other 'suitable' candidates. I have a male ancestory who on marrige took the name of his more illustrious wife - their first born had both family names.
Certainly this kind of behaviour would have been reasonably common in the 1700's I would be looking for Bethel connections.
Good luck
