Why is it called "hamburger" when, according to the story, the first burger is made of beef?

Hamburger in German would mean from the city of Hamburg. Steak tartar and similar dishes became popular in the port of Hamburg which is how the city became associated with ground beef dishes. The hamburger itself was invented in America. -burger now is used as a suffix for various sandwiches made of ground ingredients but this came after the popularization of hamburgers. Similarily Budweiser means someone from Budvar Czechoslovakia. A long trademark dispute has been going on between Anheuser Bush and a brewery in Budvar in the Czech Republic. Both companies sell beer called Budweiser; Anheuser Bush correctly points out that they used the trademark first while the Czech brewery points out they actually are from Budvar so it is a descriptive name in their case. Currently the Czech brewery sells their beer in the US as Czechvar which is a far better beer than Anheuser Bush ever dreamed of brewing and currently is my favorite lager. When I was a lad something many people claimed is that ground beef in the city of Hamburg was known as Salisbury steak while in Salzburg was known as Humburger. Probably not true though.