The Z was added so that the viewers would not be confused. The original manga was called Dragon Ball which spanned from when Goku was a kid to the defeat of Majin Buu. Akira Toriyama simply added the Z to avoid confusion. GT stands for Grand Tour, it even is said during the american version of the theme song. Z does not stand for anything, it was used to seperate the beginning of the Dragon Ball series from mid-point of the series. As stated by Akira Toriyama in an interview.
Zen is the currency used in Japan. If you were to explain Zen in other definitions, it simply can not be explained, other than "enlightment", "energy" or "calmness of the mind".
Edit
It has been stated by the characters in the series a few times that they call themselves the Z warriors; I believe they have called themselves the Earth Special Forces.
If I can remember correctly, Yajirobi was talking to the press about being the leader of the Earth Special Forces. That happened after the defeat of Radditz if I am not mistaken.