When one, often under the affluence of incahol, makes a complete fool of oneself, and disgraces one's family name. In a sense, one throws one's name into the gutter, along with any self-respect or dignity.
Bro 1: Dude, I was so trashed last night. Did I do anything embarrassing?
Bro 2: Bro, you threw some serious name. I don't think they'll ever let you back across the border after that.
Bro 1: Wait, I'm not even in the same country any more?!
or
"Man, I'm amped for this party, but I don't want to throw name like I did last week. I need to recover some dignity..."