XX621,
My understanding is here in David's post
the name 'Light Aircraft Pilot's Licence' (LAPL) for the sub ICAO licences
(my bold)
...your ICAO Private Pilot's Licence will still be called just that. It's the new licence tailored for recreational use and hopefully easier to obtain and retain that is going to be called a 'Leisure' licence.
Maybe I'm wrong, I've downloaded the documents but haven't started wading through them yet, but the above makes sense to me at the moment.
TOO