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1.
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!"
by beefstui April 26, 2007
 
2.
This expression does not date back to Vietnam or the 80's. it is ancient in the marine corps and is what drill instructors did up until the mid 70's
My Drill Instructor could kick ass and take names."
by daniel f ring August 11, 2014
 
3.
This is just from rumors I hear and web forums I read. I started hearing "kick ass and take names" around the late 80's. Some say it's a police expression.

It probably means that cops or your group of fighters kick the ass of your opponents. Then you "take names" of the people you beat. That way you know the name of a guy you beat. And when you meet him again, you know you can beat him up again.
We gotta go play basketball against that team of jerks, the Eagles.

Oh Yeah! It's time for us to kick ass and take names!
by Mr. S April 14, 2005
 
4.
to behave roughly and violently (from the image of an overly punitive authority figure in the military or police
All he wanted to do with his position was kick ass and take names.
by The Return of Light Joker December 17, 2007