Logo Branding Online Does Matter
Everything on your site should reflect your company name. Including your logo, domain etc. Your logo should have the domain name if possible. If your company name and domain name correspond, it may simply mean adding ".com" at the end of your existing company logo.
Not everyone will arrive at your site to the homepage. Remember that search engines often index pages deep within a site. Therefore, make sure that you include your web logo on each page increasing your branding as much as possible for the lowest price.
If I mention the word "cola", what is the first thing that springs into your head? You're probably thinking of Coca-Cola or Pepsi even though there are hundreds of other cola drinks on the market.
The reason you thought of these two companies is because they have spent hundreds of millions of dollars over the years building their brands.
The keyword here is branding. Branding is what differentiates one product from another of a similar make. For instance, what is it that differentiates Sprite from the other lemon soda drinks? Apart from minor changes in the ingredients, the only thing that is actually different is the name or "brand".
A good brand name is a powerful force in economics. It often means that the company who owns it can charge more for their products because consumers perceive the branded product to be of a better quality than the unbranded or rival product. Branding is also what causes people to think of Coca-Cola or Pepsi whenever "cola" is mentioned.