Hammacher is a fellow patient with Paul and Albert in the field hospital. He took a bonk to the noggin' one day and has been a little, well, off ever since.
We'll give the mic over to Hamm himself:
"I'm Hammacher. Yes, that's my name. I got a crack in the head and they gave me a certificate stating that Joseph Hammacher is periodically not responsible for his actions. And ever since then, Hammacher has been having a grand time."
His wording makes it unclear whether Hammacher has lost his marbles…or if he's self-aware and simply enjoying the freedom of his diagnosis.
He says that his past acquaintances "die[d] off so quickly," so his goal is to keep some friends around. This leads him to be a good—if bumbling—friend to Paul and Albert. While he scares them with talk of the "dying room," his tall tales seem to come from a good place: he's letting the noobs in how things go down in the hospital.
Hammacher also tries to cheer Albert up after he returns from the operating room:
HAMMACHER: Hello. Welcome home, Albert. How do you feel, kid?
ALBERT: All right. But I've got such an awful pain. My foot…Hammacher. Did they cut my leg off?
HAMMACHER: Of course not! How many did you have? Two? How many did you have? Two? You've still got 'em. One. Two.
ALBERT: Don't play the fool, Hammacher. Tell me truthfully.
HAMMACHER: Of course not. And you look fine. Look. See?
ALBERT: I won't be a cripple.
HAMMACHER: Now, now.
ALBERT: I won't live like that!
Again, we see that Hammacher's attempts are weaksauce—you don't lead with the "third leg" joke, guy—but they come from a good place, trying to talk the distraught Albert down from the metaphorical ledge.