You need to build authoritative pages for that name to bury the bad result that is showing up in the search results.
The best way to do this is to create profiles at places such as:
Facebook
Twitter
Google +
LinkedIn
Wordpress
Elance
Quora
Amazon (write a book)
Disqus
YouTube
and others.
Create profiles here and get activity to them. Be active on them. It's hard I know, but if there's activity on them and this is seen by the search engines, then they'll rank higher.
The more of these properties you can create, the better chance you have of pushing down that negative result.
I've also seen BrandYourself.com: Control Your Own Google Results which does actually help. I've used it for myself, and it's a nice service that seems to rank well.
If you can't get the negative result removed, then the information I mentioned above is the best way to go about it.
One more thing, sometimes the website that you are trying to push down is so authoritative that you will have an extremely difficult time pushing down that negative result. Ones I can think of off the top of my head are Yelp and RipoffReport.
Good Luck.
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