Nice puller! That taper does look very messed up. You will definately need to do some work with a file before you can put a new key in there. Even though it does look really ugly, you can probably run with it as is, as long as everything seats OK. It doesn't look compromised enough to actually snap off (worst case scenario). It is a very strange pattern of damage, what does your drum look like? It does look like the drum might have been spinning at some point in the past but why would it only spall in the center portion of the taper like that? Being a cheapskate, I would probably clean it up with a file, ensure the geometry with the drum looked OK and put it back together with a new square stock key and ignore it. Who knows when that damage took place anyways, it might have been taken apart and put back together again a few times since the damage occured with many miles traveled on it as is.

It would be silly to replace just the drum or just the half shaft while the other is damaged. If you are planning on having it for a long time, you should just keep an eye out for a good used half shaft, and when your drum ever wears out replace both at the same time. It is amazing how cheap (or free) stuff can be when you don't need it right away.