His name was never specified.
The Jeep Driver can be seen driving the Jeep into the village. The machine gunner on the back, then started firing on the civillians with the Browning M2 Aircraft .50 caliber machine gun mounted on the rear of the vehicle. The Jeep Driver is also seen earlier in the film, escorting the Tatmadaw soldiers to look for Rambo.
The Jeep Driver has mostlikely the goriest death in the entire franchise. The Jeep Driver parks the vehicle on a hill overlooking a valley where the entire Batallion is gathered below, preparing to execute the missionaries and mercenaries by means of firing squad. Lieutenant Aye is watching intently and smoking a cigarette as this is happening, so he fails to notice John Rambo sneaking up from behind. With a forceful swing from his razor-sharp machete, Rambo slices the man's head off. He then chambers a .50 BMG round into the chamber of the M2 and aims at the driver. The driver hears this and attempts to flee (or possibly surrender), however he is not faster than the bullets coming out of the barrel. The machine gun fires so rapidly that his chest is literally blown to bloody shreds in a matter of seconds. Rambo then turns the machine gun on the rest of the battalion, and starts mowing down the rest of the soldiers, allowing the missionaries and mercenaries a chance to escape and get weapons to join the firefight with.Later in the firefight, you can see the Jeep Driver's corpse, what's left of it anyway, fall out of the driver's seat. The entire chest is literally gone from the body and all that is left are the legs and bloody pulp from the chest.
The prop used for the Jeep Driver's corpse was made of red vinyl. CGI was added to make it look freshly blown apart. When viewed in slow motion, the Jeep Driver's death reveals that he is shot exactly twenty times at point blank range with .50 caliber bullets. His death spawned three seconds total.