are actually very well defined
Eh, I can't quite agree with "very well defined". Even Nazism isn't really internally coherent, it's surprisingly nonsensical, let alone all the variants of fascism straying so far from classical fascism.
But that's me nitpicking academically. Fascist organizations are crystal clear about their association, beliefs and what they want. When they heil or wear neo-Nazi symbols in a political context, there's no longer any need to doubt.
It is a concerted effort to redefine or undefine them so there is no longer a word to describe them.
Absolutely. Nazis have been made very aware that most communities reject them on sight and so wolf-whistling and pathetic attempts of plausible deniability are used to pretend they're just 'regular' patriotic nationalists (see: Musk salute, and this related salute overseas a few weeks earlier). But even then, these are paper thin attempts. "You're the real nazis!" "Oh everyone's a nazi these days!" "Actually they were a specific party at a specific place at a specific time!", you just gotta laugh.
Personally, in an ideal world (and it's feasible to test on a small scale like an organization election), I would advocate a certain kind of mass conditional democracy where everyone has the right to vote but must answer some very basic objective questions to verify they understand (e.g.) the candidate positions and election basics. The answers can all be found in an educational pamphlet published collectively with candidate approval prior to the election. The goal is to allow as many voters as possible, so long as they can demonstrate a basic awareness of the situation.