I recently had a law firm client whose law firm changed names. This presented a problem with the domain name because it had to change to reflect the new firms name. This can be a problem in the search engines if the original name has been in the index for the past few years.
If you just change names and stop using the old one, either the old name will continue to come up or if you just delete the name and stop using it, then it will eventually just disappear and you will lose all your search engine rankings.
THE SOLUTION IS USING A 301 REDIRECT
The solution I used for this law firm was to use a 301 redirect which involves editing the .htaccess file so that it redirected anyone who found the old domain to the new domain name. Its important to make the right updates to this file so that even if the user finds a subpage of your old site, they will be redirected to that same page on the new domain name.
This has worked out well and after a couple of weeks, the new name is now in the Google index and the old name is gone. It takes a little longer at Yahoo and MSN but at least the users are being redirected to the correct domain name.