I am from Quebec as well and I haven't lived there for awhile. I had my name changed on my birth certificate.
I think it helped that I did it in another province. On that note the forms say you can change it providing the proper paperwork stating your GID is diagnosed.
In my case, when I went to change my name with Service Canada on my SIN, they told me there was an error on my BC, other than the name at that time. Service Canada said I would receive a letter.
I got the letter stating there was an error on by BC (duh) and to mail this letter with the application for a new birth certificate. So I ordered a new one; I included the letter, the application, my credit card info and my registration of my name change. I thought it would raise questions of why Sarah is asking for Tony's BC.
Well five weeks later, I got my BC with my new name on it. I was shocked to say the least.
I figured Quebec is trying to lure me back or something.....
The next challenge is changing my gender marker. Everything said and done, all of this is invalidated and not acknowledged...just because I don't live in Quebec!
So I'm not a woman because I don't live there? Please Quebec, go for the peanut sized brain, not the pea sized one.
BTW: little robot questions; "What is the 1st word: Tree, Flower, Hawk, Snake:" is actually "what" and not "tree"...philosophically speaking.