Starting A New Business In Ontario

I hope someone can offer me some advice. I am starting a new business in Ontario (Canada) and I wonder how the name of the company. If anyone has used and registered the name, I heard that you can not use it. But this applies only Ontarionians colleagues, and the Canadians? Or in North America? Or in the world?

IE If a company wanted my name abroad, it means that I can not use it?

You should aim for your company to a global corporate identity. Therefore I suggest you choose a rare name in the world. More than one name can be chosen used. Registered unique name allows more brand and company logo would every product with goodwill was added to raise the price of selling or promoting your product from the market.
No, you can not use the name with another company to yours in the world. This way, you lose your business in one hand by promoting other company, and host international law even suits.