I did this a few weeks ago. Dead easy. Do it from the Motability website and it gives you the relevant log book number and then links you through to the DVLA website. Took about 10 minutes in total.
I always take delivery of a new car with normal plates, which I retain when I put a private plate on, and then when I take the private plate off towards the end of the lease it’s a 10 minute job to put the original plates back on.
The only slight irritant was that because the Motability car is in my wife’s name, the retention certificate now shows her as the owner of my personalised plate, although she can obviously assign it to a car in my name in future. The retention is valid for 10 years but I didn’t realise that it’s free to extend for another 10 years each time that period ends. This was good news for me as I have two private plates and the second one has been on retention for 9 years and I didn’t want to pay another retention fee, but I don’t have to.