File:lang en-th14-face-enemy6-face06n2.png

From what I understood, ドヤァ comes from the term どや顔 (doyagao), which refers to the facial expression of a smug person (「どや！」 being Kansai dialect for 「どうだ！」). Hence, *smugface*. It's only an idea, though. Better ways to put it are welcome.