IME you need to get an American call centre agent to properly book points stays in someone else's name (as per OB one). Then to the hotel it will appear as though your son is the Diamond member, and your name won't even appear anywhere. This could lead to an embarrassing scenario if he isn't prepared to be welcomed as a Diamond!
Non-American phone agents may just book as per EsherFlyer, in your name but putting son's name in the notes. This is pointless as it can be done yourself online so there is no need to call if that's what you want. It can also lead to problems if you have a non-UK address in your Hilton profile. If your Hilton profile has a UK address, it's fine as UK hotels won't ask for ID, so your son could just pretend to be you. But if it has a non-UK address, they may ask for ID, which could lead to a problem if 2 people turn up neither of whom is you. And some hotels in Europe which normally don't ask for ID at check-in, will ask for ID on points bookings to make sure that your points were not stolen (hasn't happened to me in the UK though). All this can be avoided by getting the stay properly booked in your son's name as mentioned above.