Bad idea imo. Just as renaming the software 'bitcoin' to 'Bitcoin Core' was also a bad idea.

Even though in this case it's less important, it's if anything an even worse choice; whereas in the case of Bitcoin, a written protocol spec with multiple software implementations is almost ridiculously difficult because of the requirement for all to be in consensus, in the case of Lightning, which is a point-to-point protocol, it's much more OK for people to not be in perfect consensus. So it's both practical and also very good that we have multiple viable implementations. Calling one "Core" is bad.