Unassuming rhymes with:
assuming, assuming, consuming, assuming, blooming, booming, consuming, dooming, fuming, grooming, looming, perfuming, presuming, puming, resuming, rooming, zooming
Unassuming sounds like:
unceasing, unconscious, uneasiness, uneconomic, unionizing, uniqueness, unisons, unknowing, unknowns, unsung