I'm dealing with a name inconsistency right now between CO and NW. CO has my name as "Mr John J Flyer Jr" and NW just has "John J Flyer". CO OnePass has been very helpful and communicative, and suggests that getting NW to add "Jr" (suffix) to my account should fix the issue (NW not showing Elite status). CO offered to remove "Jr" from my account, but suggested not to as "Jr" is part of my legal name.
Of course, fixing it is one part of the problem. The other is that I have an already issued reward ticket on NW, and my guess is that the name can't be changed.