I am in the same business. When I decided to quit my job and become self-employed, I had already made a name for myself, so I just used my name and added Multimedia Services afterwards.
I think you should have at least the word web or the word design in your company name. I totally agree because, especially for web design, essential to a successful logo, web page, etc is not making the user/customer think too much. So having at least one word in there related to what you do I think would be a good idea . You can play with the other words all you want. If you don t want web or design , choose at least one closely related word like site page etc.
I would strongly recommend that you consider what search engines are looking for. The use of the keyword design in your url is going to be important. I would suggest that you do a search on Yahoo and Google to determine which companies are coming up in the results. Look at their meta tags and URL strings and see how they are doing. For more free tips on web design and SEO...go to http://www.centerstagewebdesign.com