Photobucket Content and Google Search:
The search engines or indexes, mainly Google, crawl through all public content on the internet. If your account is public now or was public at any time, Google's search would have found it and added it to their index. If you make your account private, delete it or change any of the information in it Google's index will eventually crawl it again, updating this information, but it can take several weeks or even months for them to do this. If you deleted an image in your Photobucket account and then you searched for it on Google, you would still see the thumbnail and information on Google. But, if you click on the image you'll find that it is not available on Photobucket.com.
Below is some information to help you remove information from Google.
Google search is showing your deleted or private account info:
If your account has been deleted or if your albums have been set to Private, all of the content will have been completely removed from the Photobucket.com domain, along with your name in the titles of any images.
But, you can attempt to expedite this by submitting the removal of the thumbnail.
Here is some help to get you through submitting the request to Google:
1) Go to this Google help page and follow the instructions - http://support.google.com/webmasters/bin/answer.py?hl=en&answer=1663691
2) The URL for the image that was deleted will look something like http://XXXX.photobucket.com/profile/XXXXXX/XXXXXXXX.jpg. You'll need to copy this some how from the Google search when you see the images.
3) It will say that this image/page is not live, it'll ask for some text on the page, you can enter photobucket for it to search for the cached version.
Google search is showing your name from your account:
To remove your name from the public search, log into your account. Click on your username, then User Settings and you'll land on the Personal tab. You'll see a box near the bottom of the page stating, "This information is PUBLIC and anything you add is viewable on the Photobucket website." Removing your name from here will also remove your name from your library where it says "John Smith's bucket".
It may take Google and other search indexes a few weeks to have your name removed from their search indexes. You can search their help sites to find out how to make those requests. For Google, the requests can be made here. Follow the steps above.
If you do not have access to your account you can walk through the process to recover it here.