If the nature of your business demands that you have different names for your company and products or services, you should do the best you can to connect them together. Microsoft has done this extremely well. Users might not know the difference between Word and WordPerfect, but most know Microsoft. Another spin on this is to associate your own name with the product or service you are offering. This is particularly important if your business is consulting or professional services.
People are likely to engage someone they know by reputation.
The main objective of a name is clarity and recognition. The average person is bombarded with over 3,000 messages and brands every day. You want to reduce buyer confusion and indifference through the use of your name. You want to stand out. I try to avoid listing do s and don ts.