It's OTC in the UK, I falsely assumed it was the same status in Canada as in all the many discussions I've read on getting hold of it, I've not heard getting a script mentioned.
However, when you get a prescription filled in the US they don't do much checking, you certainly don't have to be a citizen to fill a prescription, I've never filled one without insurance, so I've always handed my insurance card over as ID, but it's certainly not an issue for DH to pick one up and they don't ask who he is before he signs the sheet and I don't see any evidence of them checking from the signature that he has the same surname. I think they accept knowing the name and initials as sufficient evidence of being authorised to collect the prescription.
Having not collected a prescription in Canada, I can't say what checks they use there, but I'd be surprised if they are asking for photo id for all prescriptions. When we collected scripts in the UK they'd ask us to confirm the address, so as long as name and address matched you'd be fine, allowing you to collect for friends or relatives without a problem.