What's this badge?

The badges displayed next to players names are the badges those players selected to be displayed next to their name from the set of badges that they earned for completing personal campaigns or participating in special events.

To see the full set of badges go to your garage, click on your name in the top left, then click on the empty square right to the left of your name. This will bring up a complete list of badges, showing which ones you have unlocked and which ones you do not have.

The one you highlighted in your screenshot is the "Gambit Hero" badge, which was awarded to all players who were in the top 10% of operation gambit which was a event on the global map.