But if you apply for name change first, you will have to wait for until your name change is approved/completed before you can use the new name in you citizenship application, that will delay your citizenship by as much as 3 months (my guest).
On the other hand, if you apply for citizenship first, can only use your current name in your citizenship application form, but you can simutaneously apply for your name change to provincial goverment, and i will assume name change approval will come out well ahead of your citizenship application, but as long as you do not request CIC to amend your application form, i don't think it will cause any delay to your citizenship application. Once you receive your citizenship certificate, you may rrequest CIC to amend your new name.

Hope my understanding is correct and if anyone has a better knowledge in this matter, kindly advice.