There are multiple origins for the name Bangle.I just read one post where some Spangles from Scotland dropped the S when they got here and became Pangle.I've also seen my ancestors name turn into Bangle in Quebec.He started out as Johann Adam Bengel from Germany.He dropped his first name and when he died, he was Adam Bangle. His daughter ended up being called Catherine Pingle on one ancestry page.Others became Bingle or Pangle.It depended on how the person writing it down heard it.In order to find the origins of your particular Bangle line, you'll have to dig some more and find out who carried that name in the 18th & 19th centuries.
Bengels from Germany settled in the Stone Arabia, New York area.They were given land in 1702 by Queen Anne.They naturally fought in the King's Army during the Revolution. Afterwards, some migrated to Canada and some went south to Pennsylvania and the Shenendoah Valley.I've found references to a Johann Heinrich Bengel whose name became John Henry Bangle or Bingle. He came over on the ship Francis & Elizabeth 21 Sep 1742. If you have any ancestors from Virginia or around there whose first names are John Henry, you might be descended from German Bengels.