In an interview with Animation Magazine, Trey Parker claims that the name "Cartman" came from a guy that he and Mat and Stone knew, but that the real Cartman is nothing like their character. I didn't know that "Cartman" was a variation on the name "Karpman", though.
The 1st name Eric most likely came from Eric Stouch (sp?), another friend of Stone's and Parker's who's surname was given to Butters.
"Tiberius" is also Captain Kirk's middle name.