First I am an Omnivore, but I do not turn my nose up at other ways of eating.
There is an incredible vegetarian restaurant in my town that offers Gluten Free, Dairy Free and/or Vegan dishes. The food across the board is incredible, made in house, and I would guess that 75% of their customers do not identify as vegetarian or vegan.
They do not use the word burger, they use the word patty to describe a round puck shaped portion of food that may or may not be served on a bun.
The local bagel shop has an incredible veggie patty that you can have served on a bagel or with a salad. It does not try to emulate beef, it is delicious in its own right.
Hamburgers are named for Hamburg in Germany, not the meat within them.