Good Online Business Names

Is this a good idea to have your site name (trade name) and name of the company different? Why?
I am starting a business online and you want to know if I have a company and then attach my new business to this company. Or should I have a company name which is the same on my new site / company. Is it important?
I do the same thing. Let say a customer wants to see your sites. Let's say your company is called "Ferfabo" (Random, I know). Your site is called ilikeicecream.com. (Random, but it's so different). They seek for your business, and no results come up. They get angry. HIH!
Setup a Small Business to Sell Online – Tip # 3 & 4 – Your Business Name
