Most likely originated in the armed services, probably during Vietnam. "Kick ass" is generically applied to beating the opponent, whereas taking names refers to killing the enemy, or "taking their names." Has been adopted into common usage as a general motivational statement.
"CHARLIES OVER THAT RIDGE, LETS KICKASS AND TAKE NAMES!"
"pick up that goddam football damnit! now get out there, kick ass and take names you pussy!"