The simple answer is that the hamburger was named in Hamburg, Germany. Interestingly enough, the name frankfurter (or hot dog) came from Frankfurt, Germany.
In the early 18th century, some Germans who traveled to Asia noticed that the locals there would place their beef between their saddles while riding horses, to help soften it for later consumption. The Germans loved the idea of soft seasoned meat, so they brought the practice back with them to Hamburg. As time went on, it became known has Hamburg meat.
Later, when German immigrants came to the United States, they brought the recipe with them. The first recorded mention of Hamburg meat in the US was by the Boston Evening Journal in 1884, calling it “Hamburg Steak”. Naturally, American cooks were quick to put their own spin on the dish. Charlie Nagreen is credited with making the first “American Hamburger” in 1885 at the Outgamie County Fair in Seymour, Wisconsin. However, his hamburger was not on a bun and certainly didn’t have any cheese or bacon. Poor guy didn’t know what he was missing. As with most great things in history, the hamburger took some time to progress in to what we call it today. The first hamburger on a bun was found at the 1904 World Fair in St. Louis.