Papyrus is the brother of Sans, and the most cheerful monster in the current situation. He is one of the few mostly safe monsters, as he does not outright attack Aliza.
His eyes are really small and sunken, and his scarf is torn. His teeth are crooked and dirty from something red. (Either from his "special spaghetti" or blood) His bones and and body has grown due to his 'Special Spaghetti'.
He is still very cheerful and nice monster in his personality and demeanor. He doesn't dislike humans, but he is willing to kill and eat them without hesitation. He still has a bubbly outlook, but he has become much more outright morbid and dark in both his speaking and his puzzles.
Sans warned Aliza about Papyrus, and told her to hide behind a corpse. Then, he tells Papyrus about Aliza, and lets Papyrus find her.
At first, he was happy that he caught a human. But then he became suspicious, because it was too easy. He assumed that Aliza is trying to lower his guard, so he ran away to prepare some puzzles.
At the first puzzle, Aliza died, because Papyrus argued with his brother instead of properly explaining rules to her. When she loaded her save, she solved it, surprising Papyrus.
At the second puzzle, Aliza died while Papyrus was explaining the rules in a rather unhelpful way.
When Aliza loads again, she asked for a Freebie, so Papyrus had to help her. Then he appeared when he was offering her his spaghetti.
He stops Sans from giving into his hunger by (rather comedically) punching him and stating it shouldn't be considered murder because Sans asked him to.
Sans - Their relationship is pretty much the same. Papyrus thinks that Sans is a "cheery fellow". Sans was the one who got him into eating humans so he wouldn't starve to death.
Undyne - She is described as rather abusive to Papyrus. He seems to be really terrified of failing her. He always wants to avoid being "trained" by her.
Aliza - When she encounters him for the first time, he will offer her spaghetti. Then she must solve five deadly puzzles. If she survives, Papyrus will give her Medal of honor, which allows her to interact with other monsters at Snowdin. He never attacks her directly.