A unique business name is effective in two ways. The first is that it makes your company memorable to clients and business associates. The second is that it becomes a conversation piece that gives your company character. An interesting story about the name of your company can help open up other avenues of communication with many kinds of customers.
You can take the most common business name in English and make it into a unique name by utilizing foreign words. For example, the Smith Balloon Company becomes Smith's Palloncino Company when you use the Italian word for "balloon" in place of the English. You can get very creative with foreign words in your company name, but try to retain enough of the English so that customers do not get confused. For example, the Italian word for company is "azienda," but using that to make your name unique could also get customers confused.
Using historical figures in your company name can help you to create a fictitious back story that would entertain customers and make your company memorable. For example, you could use the popular myth that George Washington slept in many beds by naming your company the George Washington Sleep Company. If you manufacture or sell axes, the you could use the story about George Washington chopping down a cherry tree and call your company George Washington's Axe Company. You should consider two things before naming your company in this way. First, you want to use the person's or fictitious character's entire name to make sure your point gets across. The second thing to do is make sure that you do not need to get permission to use someone's name or a character name in your business. Consult a copyright attorney to find out if you need permission to create your company name from a historical figure name.
Write down words that apply to your business, or words that apply to things you like, on separate pieces of paper. Put those pieces of paper into a box, and pull out three pieces of paper. Arrange those pieces of paper in several different ways and write down the names you come up with. You can include things, including your favorite colors, favorite cities, favorite kinds of trees and favorite numbers in with words that apply to your industry. If you sell construction equipment then you may wind up with a combination, such as "Blue Greased Wheel Construction Company." It is unique and you can create your own story to explain the origin of the name to tell customers.