You might not be able to do anything about it.
You see, whether or not you have any right to ask someone else who is using the same business name that you're using to stop using it depends on what level of name protection you have, so to speak.
People think that just registering their business name means that they're the only ones entitled to use it, but that's not true. Sole proprietorships and partnerships are the easiest forms of business to set up, but registering either of these forms of business gives absolutely no business name protection. Anyone can start a business with the same or a similar name if they wish.
Incorporation, on the other hand, does give some business name protection. When you incorporate your business provincially, that business name is reserved for your use in that province.
But note that I say "in that province". Someone in another province (or elsewhere) could still register and use that name if they wished. For fuller business name protection, you would have to incorporate your business federally, which would give you the right to use your business name throughout Canada, or incorporate your business extra-provincially in each province that you do business in.
See How to Incorporate Your Business in Canada for a fuller explanation of provincial versus federal incorporation and an explanation of the steps necessary to incorporate your business.
Trademarking your business name is another avenue you may wish to explore if preventing others from using the same business name as yours is important to you. Having a registered trademark gives you the right to initiate trademark infringement proceedings in either the provincial or federal courts.
It still, however, does not automatically protect your business name outside of Canada. The Canadian Intellectual Property Office advises, "If your products are sold in other countries, you should consider applying for foreign registration. Contact a trade-mark agent or the embassy of the country in question to find out about procedures. "
More on Business Name Protection
- Domain registration and name protection
- Trademark Registration in Canada
- How to Select a Good Trademark
More on Incorporation
- Should You Incorporate Your Small Business?
- Types of Corporation and Corporate Tax
- Getting Your New Corporation Up and Running