The man -- who tried funneling a drink down the woman's ass -- has been ID'd as Joe Boyett. He, along with Mary Sweat, were arrested for misdemeanor public indecency ... after video of their hijinks went viral.

As if their clowning wasn't bad enough, Mary triggered the arrest after she went to cops and complained someone had leaked the video and it was spreading like wildfire on social media. Up to that point, police were in the dark, but once they saw the video the couple got arrested.

As we reported ... Joe couldn't get the funnel to work as they partied at Rodeo Mexican Restaurant in Waycross, GA, so he tossed it and did it the OG way, right in the booth!

Boyett turned himself in Monday and Sweat turned herself in a day later. Cops have not been able to identify the restaurant staffer who gave them the funnel.

Police say another clip shows Sweat exposing her breasts and Boyett putting her left nipple in his mouth while she grabs his head and pulls him closer.

For its part, the restaurant says the behavior was completely unacceptable and "Any employees found to be involved will face appropriate action."