Hello, aux one. It's usually called an ash bucket. Ashcan (though I think it's fair to say that this term is falling out of use) generally means trash receptacle- a larger bin put out for collection. There was a group of early-twentieth-century painters called the Ashcan School, known (not surprisingly) for blunt realism.
If, in your novel, your hero is asking his American wife if she took out the ashbin, make sure she doesn't say something like "Oh! I should have done." I've often noticed this "mistake" in Brit novelists' rendering of American speech. The response to our British hero would always be simply "I should have."
Time to shovel out my woodstove!