For changing name in Indian passport you need to go through BLS international's website : http://www.blsindia-canada.com/
They may not accept your Canadian Legal Name Change Certificate. You would need to get affidavit for name change and newspaper advertisements in India. Check the link mentioned above.
As far as I know, Canadian Legal name change certificate would be sufficient to change Canadian IDs like, PR card, drivers licence, health card, credit cards, bank accounts etc.
I will tell you my story.
I went for legal name change in Canada after arriving here in 2011. I applied for name in change in 2012. Once i received my legal name change certificate, I went to get my drivers licence, health card, sin card, bank accounts, credit cards, pr card changed to to my new name by using the canadian name change certificate.
Then I went to BLS and applied name change on my Indian passport and got newspaper ads published in india and made affidavits. Then i got my indian passport renewed with my new name.
I applied for citizenship in 2014 with my new name because all my ids were already updated with my new name before applying for citizenship.