The name Uzi should be spelled with double "Z" - Uzzi, since in the original Hebrew name there is a Dagesh ((Hebrew grammar) dagesh (diacritic dot within a Hebrew letter) : emphasis) which should double the letter in other languages like in this case English.
A character on the Royal Tenenbaums is named Uzi, who along with his brother Ari, are grandsons of the title character Royal, sons of Chas (Ben Stiller).