The name Peanuts was a great frustration to Charles M. Schulz, whose original title for the strip, Li'l Folks, had to be changed for copyright reasons (and not because it's a candidate for lamest title ever). This led many new readers over the years to assume that Peanuts was the main character's name. (Beyond this, Schulz simply didn't like the title, which had nothing to do with the comic; this is why the names of collections, TV specials, and so forth usually avoid "Peanuts" in favour of "Charlie Brown" or "Snoopy".)
In fact, for many years the Sunday strips added the subtitle "Featuring: Good Ol' Charlie Brown" to the title to avoid confusion.
The Brazilian version tries to justify: Charlie Brown is nicknamed "Minduim" (from amendoim, "Peanut").
In Argentina, the strip was always known as "Snoopy". In Spain, too. And Japan. And Hungary. And Sweden. Makes sense, I suppose.
In Israel it's "Snoopy And Friends" and no, people do not think "Friends" is a character.
In some Spanish versions, it's simply called "Carlitos" (i.e. "Little Charlie").
Other Spanish versions name the strip "Rabanitos" (little radishes). How they got from peanuts to radishes is beyond me.
In Denmark, it's called "Radisierne"—"radishes," again—supposedly because there is no word for "peanut" in Danish.
The animated specials run into confusion from the other side. That is, they're called "Something Something Charlie Brown" even if Charlie Brown has little to do with them. For example, "She's a Good Skate, Charlie Brown" focuses on Peppermint Patty preparing for a skating tournament. Chuck just shows up as a crowd extra at the end.
Zits is not a nickname for its main character, Jeremy; it describes the fact that Jeremy is a high school student going through adolescence.
For Get Fuzzy, some people think "Fuzzy" is the name of the cat. It's actually Bucky.