Yes, they want you to use the name that's on your passport, so presumably if someone were submitting an application soon after marriage and wanted to use their married name on the application, they'd want to quickly change their passport to their married name first.
I used my maiden name on my application as I'm going to Quebec and they require you to keep your maiden name for all legal purposes. I believe I still could have submitted my PR application with my married name so long as that was shown on my UK passport but I think all I would have ended up with is a PR card and SIN card showing my married name and a driver's licence and health insurance card showing my maiden name, and that doesn't seem like a smart idea.