(The backstory here is that a lot of similar Jewish names got turned into "Cohen" at Ellis Island, where a lot of Jews were coming into the US because of all the pogroms.)
Edit: I'm being told that the Ellis Island changing names thing isn't true? The more you know.

Today, members of many white ethnic groups – including Jews, Italians and Poles – believe that insensitive or ignorant Ellis Island officials changed their families’ names when they arrived in the U.S. to make them sound more American.
Some last names are much older. The REQUIREMENT to have a last name was new
Yes. But Cohen is special. It indicates patrilineal priestly descent. It's not a surname that someone who wasn't a Cohan would have chosen (the rabbis would have made sure of that).
There is scientific evidence to support this, although it points to multiple clans rather than a single founder (by tradition, Aaron).