Unisom rhymes with:
agawam, cablecomm, caricom, chipcom, datacomm, decom, econocom, electrocom, firebomb, gazprom, inacom, intercom, larcom, microcom, mishawaum, navcom, netcom, onecomm, qualcomm, rosenbalm, scicom, sitcom, soderblom, sriram, worldcom
Unisom sounds like:
uncanny, uncommon, unicom, unikom, unionism, unison, unknown, unosom, unscom, unseen, unshaken