I never had any problem with this. The name is as it appears on my TRV, WP, SP, Passport, Drivers license, SIN Card, Birth certificate.
Especially if you have lodged WP/SP before and you were using this exact name, this means they already have you on their "CLIENT ID" database.
The only thing is, RCMP police clearance might take longer for some reason if you have one name... so just be patient

... for me it takes roughly 3-4 weeks.