What is the oldest 'new' thing?

Loses out to New College, Oxford (as bonzer noted), founded in 1379 and known by that name since before 1400. And probably to some other structures already mentioned as well.

I know you didn’t intend this as a serious contender because the word “neutron” is recently coined. But actually, “neutron” doesn’t even qualify as a name signifying “new”.

It means the “neutral” particle, from Latin neuter which is derived from ne uter, “not one nor the other”, rather than from German neu, “new”.