cup - a small open container usually used for drinking; usually has a handle; "he put the cup back in the saucer"; "the handle of the cup was missing"

demitasse - small coffee cup; for serving black coffee

handgrip, handle, grip, hold - the appendage to an object that is designed to be held in order to use or move it; "he grabbed the hammer by the handle"; "it was an old briefcase but it still had a good grip"