Azeem /az-eem/ [2 sylls.] as a boys' name. Azeem's root is Arabic, and Azeem means protector, defender.Azeem is a version of Azim (Arabic). Compare surname Azzam.zeem is an uncommon given name for men but a very popular surname for all people (#64750 out of 150436, Top 43%). (2000 U.S. Census). Charted below is the birth name popularity of Azeem for boys.