Can you change your name when you become Permanent Resident

[NewResident]

My initial Work Permit was issued with my first last name (Perez) as my family name. This means, my first SIN card (that started with a '9'), bank accounts, taxes, driver's licence, employer documents, etc, are with my first last name as family name.

Now that I have become Permanent Resident they have put my 2 last names on the Confirmation of Permanent Resident document (Perez Lopez) as family name. My new SIN card will have these 2 last names as family name.

Since I already have all my documentation with the 'Perez' last name as family name, is there a way to keep 'Perez' as my unique last name as family name (and get rid of the second one - 'Lopez')? I see this may cause me major problems because my PR Card and my new SIN card will show 'Perez Lopez' and not 'Perez' as all my documentation shows currently.