Can a new business start in the US, if a business by the same name already exists in Canada?

If the business was in the United States this would be an easier question to answer. The fact that the other business is in Canada makes this subject to international agreements between the two countries. The US and Canada have had a long standing relationship and they do protect the rights of companies in their home countries. The first issue you need to address is whether there is the possibility that the fact you have the same name could lead to confusion in the marketplace. If the other company is a large company, they may be quick to act to get you to stop using the name. If they are a smaller, regional company, that does not sell their product in the international stage, they may not care at all that you have the the same name. Your best resource to do more research is the United State Patent and Trademark Office website, http://www.uspto.gov. If you are planning on applying for a trademark you should do so as quickly as possible. I have sued other companies and represented defendants before the USPTO office, so should you have any questions, please feel free to visit my website at www.bolegal.com.