"Prison Guard" is not an official name. It may have been referenced in the storyline as such, but has not been officially named. Alternatively, it may be a name popular among fans, but without an official basis.
The guard makes his first appearance in Chapter 4 of Recreation to tell Washington he has a call. After Washington finished the call, he demanded the guard take him to see the "commander". The guard obliged and later takes Wash to see the commander, who turns out to be the Chairman. Before sending the Freelancer in, he warns Washington if he does anything suspicious, he'll shoot him.
When the Prison Guard takes Washington to the Chairman, a short conversation is had between them that mirrors the conversation between Agent South Dakota and Agent Washington in Recovery One: Part Two.