It’s probably related to the term bangtail which I guess is a thing with horses and other livestock where they trim the tail hair straight across for reasons. Delving further into speculation it could have picked up the pluralization along a “those women with their bang cuts” > “their bangs” sort of route. I dunno man, language is weird.

Here’s another haircut example: the mohawk, also called a mohican in the UK and presumably other places, is a recognizable style independently named after two different indigenous American tribes that didn’t wear their hair like that. America picked it up from the film Drums Along the Mohawk and the UK got it from The Last of the Mohicans a few decades later.