In hindsight, I'm glad I did the medical before CIC requested it. However, there was a risk that my results wouldn't be matched up properly with my file, and I would have had to do the medical again. Not cheap in Québec!
As for the name change stuff...UGH! I feel your pain. I took my husband's name, and everything back in the U.S. *except* my passport was changed to my married name. We never had time to do the passport, as we were married in April, traveled to Québec in May for our house-hunting trip, and then started our move in July. We *might* have had time to get my new passport between the HHT and the move, but I didn't want to risk not receiving the passport in time, as I was closing my PO box when we moved, and I HAD to have the passport to cross into Canada. I will get PR under my maiden name. I can't change anything now, as we have travel booked in March, so I have to travel under my maiden name.
At some point, I'll have to get my name changed in my passport, and then I suppose I'll go to WAR with Québec for the right to use my legal, married name (they don't let women take their husband's last names here, but I've read up on it, and I'm prepared to fight for the name change). *sigh* I feel like it'll be 2020 before ALLLLLLLL of my administrative stuff is finished, lol!