There’s a lot of false information about this subject and it can be hard to parse the reality from the fiction, so let’s clear up some misconceptions.
The Z in Dragon Ball Z stands for Z-Warrior: False. This is a case of confusion with cause and effect. The main characters are referred to as Z-Senshi or Z-Warriors because they’re the main characters of Dragon Ball Z, not the other way around. There is no greater significance to the term than that. Moreover, the term “Z-Warrior” never actually appears in Toriyama’s manga. Makes sense, considering that the manga never carried “Z” in its title. Toriyama’s chosen name for the group was actually Dragon Team. The term “Z-Warrior” first appeared in the TV Special A Final, Solitary Battle: The Father of Z-Warrior Kakarrot, Who Challenged Freeza (better known as Bardock — The Father of Goku in the states), which aired in Japan on 17 October 1990, right around the time that Freeza transformed for the first time in the manga and right when Gohan, Kuririn, and Vegeta were fighting the Ginyu Special Squadron in the anime.
The Z in Dragon Ball Z was originally a 2, but was misread as a Z: False. While it is true that one of the pitched names for the second TV series was Dragon Ball 2 (among other titles like New Dragon Ball, Dragon Ball ‘90, Dragon Ball Wonder Boy, Dragon Ball: Gohan’s Great Adventure, etc.), the idea that it was misread as Dragon Ball Z is just a rumor.
The Z in Dragon Ball Z stands for Zenkai: False. Fans tend to exaggerate the the significance of the term Zenkai in the Dragon Ball franchise. While it does appear in the title of the first Dragon Ball Z ending theme Detekoi Tobikiri Zenkai Power! and in video games like Zenkai Battle Royale, it’s not the name of the Saiyans’ ability to gain strength by recovering from near-death as many fan believe. As far as I know, there’s no official term for the ability other than “getting stronger by surviving near-death experiences” or some variation of that. Moreover, it’s not the Z in Dragon Ball Z.