Ahmadis call themselves ahmadis because they consider Hazrat Mirza Ghulam Ahmad AS to be an imam Mahdi. this name is to NOT differentiate them with Muslims, since Ahmad was one of Muhammad SAW's name as well. Hence, callin them something other than Ahmadi Muslim will be offensive to them.
As per your question.. They're Muslims too, eat with them , and invite them to eat with you. If you dont feel comfortable eating with them, by all means avoid it. Personal choice.
So who ever comes up with a sir name or a family name related to our Prophet is supposed to be an authentic.
Grow up kiddo!