Am I ordering BBQ incorrectly?

I have been to several BBQ places (most frequently, truth off of Washington) and ordered brisket, but upon tasting it wished I had been served a fattier cut, hoping to find something to rival the amazing brisket i was served at Terry Black’s in Austin.

Am I supposed to ask for a particular cut of brisket as they’re slicing it if I prefer a fattier cut? Or am I supposed to just hope I get served the cut I desire?

Sorry for my lack of knowledge, I’m willing to learn if I’m doing it wrong! I just want some amazing brisket.