Hameez is a non-Quranic Arabic name that means "cute", "smart", "intelligent", "subtle". Since the meaning is good it is acceptable as a Muslim name. It is pronounced as (HUM)ble + (EASE). It can also be spelled as Hamiz, Hameiz, Hemiz, Hemeez, Hemyz, etc. The stress is on the second part of the name, "-eez".
Another name with the same meaning is Haamez, pronounced as (HA)rd + (MI)ddle + (Z)oom, with the stress on the starting "Ha". This name may also be spelled as Hamiz, Hamez, Hamz.