I checked it on IRCC website. You can update it even when citizenship application in process. They are asking for 3 thingsNot sure if doing it while ur citizenship is under process was a wise decision. Technically the name on the passport that u submitted with citizenship application and the current passport is different.. reach out to IRCC about how to tackle this..
w.r.t the letter, I did it over 5 years ago.. I am sure I won't be able to find it.
1. new passport with corrected name
2. Linking documents( new and old passport)
Only option I am confused about 3rd requirement which is
- provincial documentation in the new name to establish identity, as part of the application instruction guide to establish the person’s identity, not only the name.