Answer
This is an official answer by QuranicNames.com Staff
Aleeza is another spelling of the Hebrew girl name Aliza which means "joyful". Aleeza or Aliza is not a "Muslim" name, but Muslims can use this name since it has a good meaning.
Aleeza can also be short for the Persian name Aleezadeh, which means "offspring of Ali", literally meaning "high-born", "high in status and rank" (but Shiite Muslims use it to mean "offspring of Ali bin Abi Talib").