Update: The Starwars.com website have officially named this character as FN-2199, one of the stormtrooper trainees who served with Finn in the star wars prequel novel Before the Awakening
MEET FN-2199, A.K.A. TR-8R:
His name is FN-2199. But his friends call him “Nines.” As detailed in
Greg Rucka’s excellent book Before the Awakening, Nines trained and
served on a squad with Finn (then FN-2187) in the First Order. That
explains why he seems just a little extra angry upon seeing Finn
during the attack on Maz’s Castle. You can see FN-2199 in the image
below by Phil Noto from Before the Awakening — he’s the trooper seated
in the background with red hair. Who’d have thought?
Hat tip to @AlfredoHernández
There's not been a character name released for him yet. The official Star Wars Databank refers to him as...
"Riot Control Stormtrooper"
and the screenplay just refers to him as "Stormtrooper"
FINN SURPRISES A STORMTROOPER WITH THE LIGHTSABER, then another!
Untrained, he's athletic, brave, impressive. One Stormtrooper has a
FINN and the TROOPER WITH THE MACE battle. The Mace Trooper KNOCKS
FINN DOWN! The Stormtrooper is about to end him, when THE STORMTROOPER
IS SHOT AND FALLS!
He's not named in the film's junior novelisation
The troopers were as startled as Finn when he sliced through armor,
bone, and flesh. Two he cut down immediately. The third trooper
dropped his rifle and brandished a melee weapon of his own, a riot
control baton that crackled with blue electricity. Finn swung at him,
but the trooper ducked and shoved Finn backward, off his feet. The
trooper had raised his baton to finish Finn when a blaster bolt
finished the trooper instead.
Nor in the Official Novelisation
A third came at him with a close-quarters weapon and the two locked in
combat. Despite lack of any training with a lightsaber, Finn was
athletic and courageous. In tandem with such traits, the saber made
him a formidable fighter.
The trooper who had engaged Finn was big, strong, and agile. Finn
realized the fight would have long since been over if not for the
trooper’s regard for the lethal potential of the lightsaber. That
didn’t stop him from finally knocking Finn to the ground and raising
his own weapon for a killing strike—only to fall backward, shot before
he could deliver the blow.
Nor in any of the film's official merchandise