TMZ stands for

"thirty mile zone". I googled it after they were in the news so much lately and found out that "thirty mile zone" stands for the geographic area with a thirty mile radius of downtown Hollywood. It's a film industry trade term for the area that companies do not have to pay extra transportation costs during production.
Obviously, it's supposed to represent how TMZ is on the "inside" of Hollywood stories.

Not advocating for them or their "journalism", obviously. I just thought it was interesting.