There is no need to be sorry. You're just new here
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No a province has to initiate the change. So, when you get your PR Card, submit the Name change request, and supply your marriage certificate, and your NFLD DL. That should be enough. I would wait until you have your card though -- to avoid confusion.
CIC and Service Canada are unconnected. The responsibility for CIC is refugees and immigration concerns. A name change is a provincial government concern. Remember: Canada is a federation of provinces and territories. So, the provinces manage little things like names. The federal government will take the change, based on the ID provided by the province. I believe in Quebec, they do not permit a partner to take a surname because of marriage -- I could be very wrong here, but I remember reading something of the sort. Just goes to show you exactly why CIC is not concerned.
Once you're landed, you can mention to Service Canada that you have a name change happening (show your NFLD DL). They should be able to automatically apply that to your CRA account (that's who issues the SIN).