The Hawks supporter's name is Jose Lozano ... and he tells TMZ Sports the incident all happened in front of Xtadium in downtown Seattle on Sunday at around 1:30 AM.

Lozano says he tried to get a pic with Lynch inside of the bar earlier in the night -- but was denied by the Seahawks legend's friends ... who told him straight up, "No pictures."

However, when Lozano spotted Lynch outside of the establishment a short time later, he made one final attempt to get the former Seattle tailback to stop for a photo before he called it a night.

In video from the scene, you can see Lozano approach Lynch -- who's wearing a Beastmode sweatshirt -- and yell, "Marshawn! Beastmode! Let me a take a --."

Suddenly, though, Lynch appears to lunge at Lozano's phone -- before the footage cuts out.

Lozano tells us once the camera stopped rolling, Lynch grabbed his phone and screamed, "Y'all mother f***ers are weird," before he busted up the device with his hands. Eventually, Lozano said he was able to get the phone back just prior to Lynch leaving the area.

Lozano tells us he didn't realize his phone -- an iPhone 14 that he purchased just a few months ago -- was broken until several minutes had passed, but he said he has no intentions of going to police now over the incident because he's such a huge fan ... although he did say he wished Lynch hadn't been so "rude."

This, of course, is not the first time Marshawn has been accused of swiping at fans' phones ... back in 2017, he smacked a phone from a man's hands while out at LAX.