So, when I did it, I was a PR for 2 years, but only 6 months in Canada/Ontario.
1. Submitted an application to Consulate for passport renewal with correct name and a letter explaining the issue,
2. Submitted PR card renewal form to IRCC with all necessary documents + copy of letter submitted to Indian consulate, similar letter addressed to IRCC + Copy of old and new passport showing a link (old passport will say cancelled, and last page of new passport will have old passport no.)
3. Once PR got updated, submitted a request to edit DL, OHIP and SIN.
Whole process took about 4 months during pre-pandemic era! Please note, only your PR Card gets updated, COPR never gets updated