I need help! I own a display company called Adfab Exhibit Group Inc.
and have a website (www.adfabexhibits.com) which we registered with
the Google search engine a few months back. Adfab Exhibit Group was
formerly called ADfab Design Group and we also had a website
(www.adfabdesign.com) registered with the Google search engines.
Recently we have completely removed our Adfab Design Group website
from the internet and cancelled any hosting etc associated with this
name. The problem is that whenever  a search is done through
Google.com for ADfab Exhibit Group (the newer name) the found site is
ADfab Design Group (even though this site no longer exists). As a
result we cannot successfully be found on Google AT ALL via ADfab
Exhibit Group. The two site had different domains and were two
completely separate site. Why and how is Google finding ADfab Design
Group when searching for  ADfab Exhibit Group, and why is it unable to
find the actually website for ADfab Exhibit Group. What can we do to
rectify this problem.
(www.adfabexhibitgroup.com) at all.

It appears that all you need to do is wait until Google next updates
their index. I suggest re-submitting your site just in case. The only
place to do it is:
://www.google.com/addurl.html

Thanks for your comments Robert. We have been waiting patiently for
almost 2 months now and I'm sure Google has updated their index since
June. Neverthless I will take your advice and
re-submit the site again. Cheers :)

It often takes two months. When you submit, there's perhaps a 50/50
chance they can fit you into their crawl schedule before the next
update - so sometimes the pattern is:

submit > your site gets crawled > update

and sometimes it is:

submit > update > your site gets crawled > update

I guess patience truly is a virtue in this case. Thanks