In most cases, you will need to register your business name.
The only exception to this in most provinces is if you operate your new business under your own legal name with no additions. (Newfoundland and Labrador are the exception to this general rule; in that province, you do not have to register the name of sole proprietorships or partnerships at all.)
So if I run my business under the name Susan Ward, I don't have to register my business name.
However, this business is going to be a sole proprietorship; I can't add anything to this name, such as "Inc." or "Co." or "& Partners". Nor can I add anything that would give potential customers/clients a clue about what I do. If I decide to call my business something such as "Susan Ward's Consulting Services", I have to register my business name, even though I'm still running it as a sole proprietorship.
And not to pick on anyone's name here, but many people's names are not catchy or particularly easy to spell.
In sum, if you choose to operate your new business as a partnership, corporation or cooperative, you need to register your business name, and most sole proprietorships will want to register their business name, too.