Memes

To be fair, in common lingo, communist is pretty much 1 to 1 associated with Marxism. Socialism is more broad, and anarcho-communism is nearly always prefixed with anarcho-, due to communism being historically affixed to Marxist movements. I think if you use "archist," most won't understand what you mean.

In my eyes, the 2 most relevant umbrellas of leftist thought are Marxism and anarchism. "Libertarian socialism" is a bit of an odd one, it's closer to a non-commital anarchist than an actual coherent ideology with its own history and theory. Syndicalism is kind of its own thing, and mostly relegated to a specific historical period. Other, local ideologies like Zapatismo, or ideologies like Nkruhmahism-Touréism that are their own thing, don't quite fit in either.

So, I think the easiest answer is just "Marxist." Maoists consider themselves Marxists, Marxist-Leninists are Marxists, I think it makes the most sense that way. Crucially, what makes Marxism and anarchism the two real umbrellas is that Marxism essentially posits full collectivization of production and distribution in classless society, while anarchism posits full horizontalism and decentralized networks devoid of hierarchy within cells. These are pretty much opposite approaches, Marxism seeking liberation of the individual through liberating the collective, and anarchism seeling liberation of the collective through liberating the individual.

Hope that helps make the case for just using "Marxist." Easiest way to not be confrontational.