Souplex said:
We already have a name for it: Cartoons.
Just because it's from Japan doesn't make it not a cartoon.
To play devil's advocate, the term "cartoon" has connotative meanings that, even if the proper definition works, would render it a problematic name for anime.
To elaborate, whenever you think the word "cartoon," you most likely think of Bugs Bunny, Micky Mouse, Felix the Cat, and other mascots of old-school animated shorts. You may also think of things like Spongebob. Basically, the term implies animated shorts of zany characters doing zany things (kid-friendly or no; several Adult Swim series would fit the connotative meaning). Even though "cartoon" may simply mean animated (though I'll address that in a bit), by calling anime cartoons, you're lumping things like Gundam, Darker than Black, Baccano, and other things like that with things like Loony Toons, whether you mean to or not (not that I have anything against Loony Toons, but you can see the problem, no?). Basically, even if cartoons and anime are the same by proper definition, steps must be taken to avoid connotative issues (extrapolating, of course, you'd need to do the same thing with a good bit of western and (former) Soviet Bloc animation).