Send the PR renewal application (check the document checklist and everything)along with the copy of your current valid indian passport with the old name and copy of the legal change of name certificate(legal name change document is really important to be included)
Once you pr card is issued with new name, get your indian passport reissued with new name. You may have to follow Indian procedure for name change. They want you have Pr card's name changed before they can change your name on Indian Passport. (Atleast that's what happened to me in 2012)
In the meanwhile get all your provincial IDs changed like: Drivers licence, health card, sin card, credit cards, debit cards etc etc. by showing your legal change of name certificate.