Legal issues such as this are probably best handled by the Stack Exchange legal team. I don't think it's ideal for a community to be making legal decisions. If the owner of the Advent of Code trademark has a problem, their correct course of action is to send an email to [email protected].
But I am, of course, not a lawyer and doing the rename is definitely the safest course of action.
Keeping the community out of it also reduces the legal risks the community is exposed to. The law is weird, and it could certainly be that the act of renaming it (or the way it is renamed) may be less safe than to allow the designated legal team handle it. The mere act of taking this into our own hands may cause legal liability to change hands from Stack Exchange to us. I don't know. I am not a lawyer.
Let the lawyers handle it.