We moved our site to a new domain. Is it possible that the results that appear when someone Google our previous name, also appear when someone Google our new name?
Here is a step by step guide on what to do when migrating your website:
301 redirect your website: Make sure all of your old domain urls redirect to their representative url on your new website.
Index your 301 redirected website: Fire up Google webmaster for you old domain and perform
Fetch as Googlein order to emulate Google displaying the search engine result page.
This step is crucial in quickly getting your old brand name's website removed from search and showing the new website (mostly) in it's stead.
Because you have 301 redirected your previous domain, Google should be intelligent enough to transfer the contextual brand information to your new brand URL and it should show your new URL.
Expect some migration issues for indexing during this period; you could manually fetch every url on your old domain to "speed" up the process but that would be cumbersome for larger websites.
site:olddomain.comto check if pages are still indexed and be sure to compare this to your new website.
site:olddomain.com | site:newdomain.comshould only display results from your new domain on the first page.
However if your brand name has generic terms it is possible that you will be out ranked for your old brand name term. This gets into the whole scope of Online Reputation Management as a service where your will have to rank your domain for your old brand name terms.