Personally I don't think there is a huge problem here (and I doubt that JAXA will be particularly upset), but at the same time I am not particularly attached to the Selene name so if somebody comes up with a good, unused alternative I am likely to endorse it.
While this is topical, I will say that I have found it kind of annoying that all our various clusters of modular boosters have names (Selene 1, 2, 3, 4,…) bu the modular boosters themselves have no shorter or more convenient name than "the modular booster". This is cumbersome to write out and I'm not even sure it makes sense – I would use the term "modular booster" to refer to the actual whole assembly, e.g. Selene 3 is a modular booster. The individual components they are made out of would be better called "booster modules" – but a short and convenient name like Selene for these modules would be a great asset.
If we do want to think about different names, I would suggest that a non-lunar-specific name might be a good idea, simply because we may end up using the booster modules we develop for CLLARE for entirely non-lunar projects later on (like launching a space telescope or a Mars probe).