The problem is that I cannot change my foreign passport because I came as refugee and my passport was taken on the border. The issue is that I don’t want my PR card, and thus my Canadian passport (later on) have my husband’s name attached to mine. I want my name to be simple (first and last only). Also my notice of decision has my name without my husband’s (as per my request). Correct me if I’m wrong: so the only thing with my name on PR card is when I want to travel? Nothing to worry about inside Canada? And will I be able later to get a Canadian passport without EP husband’s name on it?
Are you still with your husband or divorced? Not that it's my business, but if you're separated or divorced, the reason to change name is established and hence (I think) a bit easier.
Now you are asking slightly different questions - I was emphasizing what name is on documents when you travel (so that you have fewer problems when travelling, but the issues of using your foreign passport as a refugee are complicated so hopefully you're not doing that).
You are asking when the name on PR card will 'propagate' (be used by other institutions). There's no universal answer to that question - but in short, if you don't show passport or PR card, not likely anyone will use that name. (Federal government may continue to use though). Eg in places like Ontario driver's license will be used by most.
At any rate, you can try this for fixing the 'error' or otherwise changing for your PR card:
https://www.canada.ca/en/immigration-refugees-citizenship/corporate/publications-manuals/operational-bulletins-manuals/identity-management/naming-procedures/managing-existing-records-change-name-request.html
If you have separated, I think Ontario makes this a bit easier (you'll have to check for other provinces):
https://www.ontario.ca/page/change-your-last-name
If general change of name, a bit more tedious perhaps but still not that complicated:
https://www.ontario.ca/page/change-name
I don't believe either of these are limited to Canadian citizens, i.e. as a PR you can still avail yourself of the procedure to change name. Federal government will accept provincial change of name.
Note, this may get VERY complicated if you ever need to use that foreign passport and can't change your name abroad - but as a refugee I udnerstand that is a very bad idea anyway. In other words please do NOT take any of this as related to what you should do for your refugee status.
Good luck.
