To become an officially recognized business entity, you must register with the government. Corporations will need an "articles of incorporation" document, which includes your business name, business purpose, corporate structure, stock details and other information about your company. Otherwise, you will just need to register your business name, which can be your legal name, a fictitious "doing business as" name (if you are the sole proprietor), or the name you've come up with for your company. You may also want to take steps to trademark your business name for extra legal protection.
Unlike in many other Western countries, Canadian businesses generally only have one form of incorporation available. Unlimited liability corporations can be formed in Alberta "AULC", British Columbia "BCULC" and Nova Scotia "NSULC". The aforementioned unlimited liability corporations are generally not used as operating business structures, but are instead used to create favorable tax positions for either Americans investing in Canada or vice versa. For U.S. tax purposes the ULC is classified as a disregarded entity.