Muslim Meaning: The name Hamza is a Muslim baby name. In Muslim the meaning of the name Hamza is: Lion. Sour leaves. American Meaning: The name Hamza is an American baby name. In American the meaning of the name Hamza is: Lion.Sour leaves.SoulUrge Number: 2. Expression Number: 22. People with this name have a deep inner desire for love and companionship, and want to work with others to achieve peace and harmony.n Muslim the meaning of the name Hamza is: Lion. Sour leaves. American Meaning: The name Hamza is an American baby name. In American the meaning of the name Hamza is: Lion. Sour leaves.