Like you, I have an unusual name. In fact, I've only been able to find one other person with my name and she works in the public schools in Philadelphia (last time I checked).
I really wish I had a chance to speak with you before you filed suit. It's not Yahoo's fault that your name turned up results for porn and malware. Yahoo only crawl's the sites that are out there, and that would have been easier to change than filling out legal paperwork.
When I got married and acquired the last name Johnson, I decided to have a little fun and get the first page of Google results to rank for me instead of the woman in Philadelphia. It didn't take long. The poor woman is now banished to the last result on page 3 of Yahoo and nowhere on the first 5 pages of Google (I got tired of looking).
"Nathania Johnson" is not exactly a competitive keyword phrase and neither
is was your name, "Beverly Stayart." All you had to do was get a bunch of social media accounts and put your full name on it. That's what I did. Blogspot and Flickr are good ones. Heck, having an account on SEOmoz will rank. Commenting on popular blogs helps, too.
Buying the URL with your name in it and publishing some fresh content helps big time.
If you really want to go the extra mile, you could have gotten all your friends to link to those sites with your name being the anchor text. Don't do too many all at once or the search bots will get suspicious. Then again, they also wouldn't have cared so much about such a little searched term as your name.
Now, a search for your name is filled with a bunch of links to sites talking about your legal case. It only took a day for that to happen, but going forward, it will be very difficult to change that. Ask any company with a negative result in the search for their name and they'll tell you how difficult it is to change this. That's why we do posts on reputation management.
I'm sorry that your name returned porn and malware sites. There is a reason Yahoo is number 2 - and I mean a distant number 2 - when it comes to search engine share.
I'm afraid you're likely to use your case. But if your true goal is to have better results for your name, do read the posts you find here at Search Engine Watch on a regular basis.