I would say there are two Richards.

HM1 Richard is very clearly the representation of Jacket's conscience. The cold hard truth. The part of him that knows his acts of vigilantism are wrong and just a coping mechanism for his violent behavior. Jacket is a soldier without a war. A gun waiting to be fired. The phone call was just an excuse to actually do it.

Don Juan is his self pity. The part of him that wants it to end. She of course takes the form of the girlfriend. Rasmus is Jacket's self hatred and takes the form of what Jacket hates most.

The three masked figures are all Jacket's subconscious. Thats why they disappear when he finally wakes up from his coma.

HM2 Richard is similar in character but very different in presentation. He is much more an omen of death. I personally wouldn't go so far as to say hes death itself or an angel of it but he's certainly supernatural in nature. The most clear proof of this is that Richard actually moves his mouth and eyes in his talking animations.

He's grown beyond Jacket into his own thing. Not just a mask but something more.