The only option I’ve found that works is the Cash Passport Mastercard from Canada Post. It's a Re-loadable prepaid card that hotels will accept for reservations and payment. As long as there is a sufficient balance on it, it looks like a regular Master Card to them.
You do have to use your real name and ID to get one but because it’s not a credit card it will not appear on a credit history search and you are the only one who needs to know you have it. Everything is online so no statements will come to your door, use your pooning email. (if you don’t already have one you should) Buy it and load it using cash at any Canada Post outlet. There are some fees but such is the price of anonymity.
I’ve been using one for this purpose for almost 4 years with no issues.