You mean they made color differences part of the story in a grayscale game? Sigh
I seriously didn't expect the "Shadow" name to be literal...
The story text emphasizes he's "dark/black" on many occasions. Likewise, his design has several key differences with Quint, and he's not acting under Wily, thus the conclusion given from the get go is that he's not Quint, but rather someone else. This Rockman tells us his name is "Rockman Shadow."
BLUES: That is Rockman Shadow, just like his name, he is your shadow. As you become stronger it will be the true enemy you face.
R-SHADOW: Didn't you realize it? As you fought with my subordinates... Every time you defeat an enemy, it gets more dangerous for you. I was literally your shadow. Don't drown in power like I did, Rockman. Keep on protecting everyone... Farewell.
ROCKMAN: I understand Shadow... I'll continue my fight from here. I promise I won't misuse my power. Goodbye.