The orderly was I believe a Sergeant Tucker, who tended Traveller while Lee and Marshall went inside the McLean House. He was attached to Lee's personal staff. He is named in quite a few accounts; I'm just not looking at one now.
Orderlies are akin to the batmen of British forces, or stewards in the Navy, and assit officers with personal details -- cooking and serving food, uniform cleaning, groomsman, etc -- as opposed to military aides de damp (or flag lieutenants in the Navy), who assist senior officers with military details.