Aside from being a letter of the alphabet, "Z" or "Zee" was also sometimes used a nickname given to individuals whose name contained the letter "Z".
Lily Sloane told Zephram Cochrane "Z, you've had enough," after he offered her another round of drinks on the night before their launch of the Phoenix. (Star Trek: First Contact)
Ezri Tigan was called "Zee" by her brother, Norvo. Her other brother, Janel, called her "little girl." (DS9: "Prodigal Daughter")
Reginald Barclay referred to his friend, Doctor Lewis Zimmerman as "Doctor Z". (VOY: "Life Line")