No affects whatsoever. See my timeline below. I was one of the fastest. If you want to do it, do it before your citizenship application. I didn't even change my PR card, knowing I will be citizen before it expires.
Hope it won't affect my timeline as well. I did it before applying and haven't updated the PR card yet as it doesn't really make sense and I am not willing to update my original passport.
Can you please confirm if you get it through smoothly without updating your PR card and original passport. Did you get your citizenship in new updated name? don't you need to send any govt issued ID proof other than the name change certificate with your citizenship application?