I can't find solid proof of it being a "real" digimon "species" nor if it really is called ShadowLeomon (some places call it BlackLeomon or DarkLeomon).

If someone could clarify it, please.

I can't speak to the name, but the form is definitely real (it's from episode 13, despite what the description says)

It is present in the games as well, particularly Soul Chaser and New Century. The only place I am finding any name changes, however, are in the Korean and Chinese versions. In both English and Japanese it is simply called "Leomon". Given even small permutations in Digimon can render them a new species, and this is a very old cosmetic difference that has no cards of any kind, nor a Digimon Reference Book entry, it does not appear to be an "official" digimon, as it were, but is instead a cosmetic variant to show possession without any other differences.
It's only an adult-level, so it's unlikely there's much to really work with, from an in-universe perspective, so it's probably just intended as a viewer-benefit thing.

Given it's all we have, for the moment, and it's semi-official in the Korean and Chinese localisations, it's kinda the only name we have to go off of for that variant at the moment. They call it "Dark Leomon" in those versions.