I'm seasoning and cooking a prime rib for 10-12 servings. One person can't have garlic. Can I cut 1 piece off, (season it without garlic), and cook it separately in the same oven at the same time as the main prime rib?
Yes, you can cook it separately, assuming you are roasting it you'll need to add the smaller piece later as it will cook much faster. If you are braising it you would cook it for a similar amount of time.
My main concern would be having a small piece dry out, you're essentially talking about roasting a steak, which I'd never recommend. If it were me I'd leave the garlic out of the roast and put it in a sauce instead, or just leave it out entirely.
Sure you can cut off one piece, but there is a high chance that the one piece doesn't turn out like the rest. (It may turn out better!) I suggest you take a different strategy where you can ensure that the whole roast is cooked perfectly:
Suggestion 1: To keep it simple, make the whole roast without garlic. Then roast a head or two of garlic in a foil pouch and incorporate it into to a sauce which can be added while serving. This will still provide the garlic flavors to your tongue and nose.
Suggestion 2: Do a real side-by-side comparison as an experiment where your guests are the judges. Divide the meat in two equal pieces, one seasoned with garlic, one without. Cook them the same and then do a taste test with your guests with the goal of hopefully learning.
Suggestion 3: Substitute garlic with something else. Perhaps a similar or different flavor profile: chives, shallots, ginger, cumin, etc. Ask the non-garlic eater if they have any suggestions for substitution. (Would black fermented garlic be ok?)