In the Mickey Mouse cartoon world, anthropomorphic animals all seem to be named after whatever kind of animal they are. Thus, we get Mickey Mouse, Donald Duck, etc. As far as we can tell, these names really are intended to act as family names. (Note that Pluto, the only animal on these shows that acts like an animal, also has no last name.)
For starters, most of Mickey's family also shared the name Mouse with him. One exception is his older sister, who in turn has two younger children. All three of them are named Fieldmouse, implying that Amelia Mouse married someone named Frank Fieldmouse (who has never been shown in a cartoon, so we don't know).
In addition, Mickey has starred in a couple of cartoon shorts where he's been referred to as "Mr. Mouse", such as the early short film Mr. Mouse Takes a Trip. This only makes sense if that's his last name.
If Mouse is his last name, though, it's a very common one, because everyone in Minnie's family also has the last name Mouse: Marshal Mouse and Matilda Mouse are Minnie's grandparents, Marcus Mouse is her father, and so on.
Other "families" follow the same pattern: all of Donald's relatives are named "Duck", except for his distant Scottish relatives the McDucks. There are also family friends of the Ducks named the Goose family, the Gander family, etc.
The most interesting case is Goofy -- originally he was Dippy Dawg, but is mostly referred to as just Goofy on-screen. Over the years, he's been alternatively called Goofy Goof (implying that Goof is his species), or Goofus D. Dawg. But officially, he seems to be the only major Disney character that really doesn't have a last name.