Sole proprietorship: should I register my personal name?

Your personal name is already registered by your birth certificate or whatever immigration paperwork you have with the government.

You register a business name when you are not carrying on business in you personal name.

Maybe you want to get an HST number? I don't know.

You can definitely register a business as your personal name. For example, Let's pretend My Real Name is Giovanni LoFranco.
I was offered a job but as a Contract. One of the conditions for this is I must be a Sole Proprietor. So I go and open a GST/HST account under my legal name, there is nothing wrong with this, it is simple, then when the business pays you, you do NOT need a business bank account, you can cash or deposit cheques into your personal checking account, which I checked by the way, it is perfectly legal to put your business income into your personal account so do not let people tell you its wrong, plus you save on fees, cus a business bank account most definitely requires fees, and when the work pays you, they do not pay you a personal cheque, they remit you a payment to your business, which happens to be your real name, so you can bypass a lot of those fees, just remember to declaire it as income and pay the necessary gst/hst on it and your good. trust me, I had to do this ,but the only thing I was lying about is my name I would never post my real name on here.