Yes, that is the correct name to use for the cheque. As for insurance, there is an ICBC broker there that can get you set up for basic insurance. Just tell them that you're doing the optional insurance through a 3rd party and they'll have you sign a waiver - you then need to call your other provider and give them the info (registration number, etc.). I went through BCAA for my optional and had set up most of the policy ahead of time to speed things up. My BCAA agent then emailed me the forms, who I forwarded to my delivery advisor to print out. After signing it, she then scanned it for me and emailed it back to my BCAA agent. Once I got confirmation from BCAA that it was all in place, I was good to go. You'll want to make sure you can work with Belair during your delivery appointment (hopefully it's during work hours). It's a bit more complicated than doing optional through ICBC, but so much cheaper!
I've also heard of people just accepting the ICBC optional coverage during the delivery process, and then cancelling it once they switch over to their 3rd party coverage. That may be easier although I don't know if there would be any extra cancellation fees involved.