TIL it’s called eponym[1]. Diesel engines, pasteurized milk, Petri dish, even mentors, … I can tell you it’s much less common in ideographic languages, as the definition can be encoded into spelling by choice of ideographs, if that is what you would appreciate :)
Just because you see something in "weeb culture" doesn't mean it's unique to "weeb culture". Naming things after people happens everywhere, even in programming, booleans, bezier curves, Turing machines, etc.
These terms come from Sakuga scene where artist attribution and appreciation are a big part of it. See also "Yutapon Cubes", for example.
Also we absolutely do identify art styles after their creators if the style is distinct enough, but doesn't necessarily establish a new branch, e.g. Escher, Warhol, Wes Anderson.