As I have said on other threads here and elsewhere, we tried to get the name 'Light Aircraft Pilot's Licence' (LAPL) for the sub ICAO licences last year when the change to the Basic Regulation (from 1592/2002 to 216/2008) was going through the Brusssels process. EASA supported this, but during the Council / Commission / Parliament debates our (Europe Air Sports) request was overlooked - I believe by genuine mistake on the part of the Commission. It started life as a RPL (Recreational Pilot's Licence). In the working groups we said we did not want that or 'Leisure Pilots Licence' for the reason you mention, and also becuase of the image it might conjure up in ATC. Hence the preferred LAPL.
To get that changed now will unfortunately mean a change to the Basic Regulation (primary EU law), not the Implementing Rules which are now been consulted on through the NPA. The Basic Regulation lead time for changes can be up to three years. However, I have it on my list of issues to take up in Brussels this year, and maybe, just maybe, we can piggyback a correction from LPL to LAPL on the back of the next change to the BR for ATM in less than much less than 3 years.