Maybe Chuck wrote it, maybe he didn't - but is it a hint as to why Saul changes his name?
"I'm proud we share the name McGill" - Chuck MAY have felt this way when Jimmy was working in the mail room, but I don't know why he would have even written the letter at that time as I don't think he was near death at that time.
If the letter was changed by Kim, I could see the original letter saying something like "I resent that we share the name McGill". If Jimmy ever found out about this, I could see that pushing him even more towards changing his name. But I don't see Kim as the kind of person that would forge the letter, not just because it seems out of character, but because I don't think she'd be good at it.
Or maybe the letter is authentic, and Jimmy is driven to change his name just to spite Chuck beyond the grave. I don't think Jimmy would do this though.
Or does Jimmy end up changing his name for some unknown reason? Perhaps he does something foul and gets a cease and desist letter from the McGill Scholarship committee and just changes it rather than fight it?
Do you think the letter is related to the name change, or not?