For the larger events there are individual presenters and even troupes of "famous generals," basically hobby presenters but available for hire. These "generals" typically don't have any actual rank in the reenacting units.* They are hired to be in camp and available for spectators ('taters in reenactor-speak) to engage with, and typically are assigned to make a presentation at a central location twice a day or so. They do show up at the battles, but typically at the end of the battle and typically just for show. Sometimes they'll "review the troops" at morning roll or field parade, but again they have no real rank with the unit they are reviewing.
In my experience these nominally-professional generals do tend to know quite a lot about the person they are portraying and can stand up to some very particular and even intense questioning.
Another factor is regionalism. In my experience there is one "Gen'l Grant" per region, and he is the one **usually seen in, say, Eastern Ohio. The various "Gen'l Grants" have likely over the years crossed paths and often know each other, but there's a kind of unwritten expectation that the Eastern Ohio "Gen'l Grant" won't actively market themselves to get their foot into a, say, Western Ohio or SE Michigan event.
Of course no one controls the gig, so to speak, so if it's known than a particular event hasn't yet signed up a "Gen'l Jackson" you go for that. It goes without saying that typically a "famous general" is only hired to portray a general that was at the actual legacy battle listed in the reenactment schedule of events for the weekend.
Officer uniforms are tailored -- meaning quite expensive -- and as a "famous general" you will never look right without being tailored. If you want to be hired at a bigger event you grit your teeth and have your uniform tailored. What that means is some of these presenters leverage their same uniform to portray an alternate general merely by swapping out a hat or shoulder boards. Some of these presenters have both a Union and a Confederate "kit" to have an even better chance of maintaining their hobby as presenters throughout the season. In the North that can mean school and living history day gigs in the reenacting "off season."
Small venues are a completely different situation. They either don't pay or pay very little so sometimes it's just a guy who came with his unit to camp and reenact with them, who occasionally switches out to portray a general or a chaplain when they're not drilling with their unit. I have to say, at this level tailoring is more of an option and some of these guys seem quite silly parodies of who they are trying to be, but keep in mind reenacting is a hobby. Some that start out this way work up to the paying gigs as they transition from grunt reenacting.
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* There are a few of these "famous generals" who do happen to hold rank in the reenacting units, but from what I've seen it's rare.
** or maybe two. For a while in my region you either got the "Grant with a horse" or the "Grant without a horse," though by mutual understanding they didn't "poach" each other's "gigs."