When you first enter into a rental agreement, your landlord may ask you for some financial information. This is a reasonable request if your landlord wants to be certain you are able to afford your rent and utilities.
If you are not able to provide your landlord with this assurance, they may require a co-signer on your rental agreement. Your co-signer will be held responsible to pay the rent if you cannot or do not pay. If you cannot provide a co-signer, the landlord may not allow you to rent the apartment.
Your landlord has the right to ask for the names of everyone living in the rental unit.
The Office of the Privacy Commissioner of Canada provides more information on privacy in the landlord and tenant relationship on their website.