First, check to make sure you can navigate to your character's profile page. You can do this from your account settings.
If you can navigate to it, you are probably unable to see your character name in the immediate list for the following reasons:
There are too many characters with a similar name to yours.
Your character wasn't one of the most recently updated characters on the site with that name.
In most cases, you will need to narrow your search to find your character in the quick search if you can get to their profile page.
Please check out this page for some tips and tricks on how to use the quick search: Search Engine Quick Search Tips and Tricks