Trolls are named after the first thing they eat. In this case, Pee Hat most likely ate a partyhat that came out of a Christmas cracker, a holiday item. The term "p-hat" is a common slang term for a partyhat.
This is seemingly corroborated by the nearby Kraka, a troll likely named after the Christmas cracker itself.
Strategy
Pee Hat has a maximum hit of 23, so it is recommended to use Protect from Melee when fighting him. His wander range allows him to be safespotted by standing near the cliffside, although players can still be attacked by other mountain trolls while in the area.
For those without protection prayers, another way to "safespot" him is to stand near the entrance to the plateau, hit him a couple times before he turns towards you, and then walk outside the spear wall, where the thrower trolls will attack you. Players can then walk back inside and wait for Kraka to lose his aggression and walk back to his usual guard position. Attacking during his walk back allows the player to land a couple free hits before he retaliates and the player has to step outside again. Damage from the thrower trolls can also be avoided by climbing the rocks east of the entrance and losing aggression with climbing boots, or standing far east on Death Plateau.
If the player is willing to wait out aggression, and the aggression zones are set up correctly, the player can use a halberd while safespotted to kill Pee Hat from one tile north of the gap in the spear wall.