Just so you're clear:

1. If you book and pay, you can earn credit for up to 3 rooms, as long as the nights for the stay (i.e. check-in/check-out) all match fully. See more here: FAQ : Points and stay credits for multiple rooms (new policy effective 30 Aug 2023)
2. If you are the one paying, then others should not be able to earn points on their account, as the expectation for Marriott crediting is that the name on the account, and the name on the card being used to settle payment match. So if you're paying, then you should do #1. I believe cfischer is implying that if they use their account, but you still pay, there will be no problems, but this isn't guaranteed (obviously a lot less likely to be an issue if you have the same surname) - There is more in the T&Cs here, but I think this basic check is done most of the time (https://www.marriott.com/loyalty/terms/default.mi#earn , 2.1b - provided the Member provides his/her Membership Number at the time of reservation or at check-in, stays in one of the reserved guest rooms, and pays for the charges)

So fundamentally, there is nothing stopping you booking 3 rooms, and then when they arrive the other guests adding their own payment card and profile details on arrival (just make sure you remind them to do that), this would often be done by travel planners and other companies, so is a fairly standard process.