A made up name, much like Hugh Janus, or Mike Hunt, that is used for a cheap laugh. It is meant to sound like "Bury my cock in her." It was made famous when the guys on the show Workaholics used it in a conversation with their boss.
Teacher: "New kid, what's your name?"
New Kid: "Barry."
Teacher: "Barry what?"
New Kid: "Barry McCokiner!"
New Kid: "Barry."
Teacher: "Barry what?"
New Kid: "Barry McCokiner!"
by Auditioning my Finger Puppets February 21, 2018
Guy: hey guess what i do every night!
Friend: what?
Guy: i Barry Mccokiner
Friend: What?
Guy: i bury my cock in her.
Friend: who?
Guy: your girlfriend.
Friend: what?
Guy: i Barry Mccokiner
Friend: What?
Guy: i bury my cock in her.
Friend: who?
Guy: your girlfriend.
by Huegh G. Rection April 3, 2015