Look at it as you would a bank account, it would be your sons account with his name as the account holder and you acting as an appointee.
Looking at my most recent Motabilty paperwork from the dealer, shows the car in my daughters name and me acting as her appointee, which explains when I had the NIP through for speeding it was in her name.
As I act as an appointee that comes from Motability states, I am acting as the appointee. Any phone calls to Motability, I’m always asked the claimants name.
Looking at it logically in your case there will be to different PIP reference’s (yours and your sons) to be entitled to a Motabilty car you need to be claiming an eligable benifit, which both you and your son do!
I can’t see a problem, but ringing or online chat with Motability explaing you are allready a Motability customer and want to be an appointee for your son, who also wants to join the scheme, with his own qualifing entitlement – will that be ok, which I’m sure it will but, more importantly will give you a guaranteed answer to put your mind at rest.