Twitter is now showing "name results" for people in search results. The feature appears to still be in the process of rolling out, as not everyone is seeing the results, but I'd imagine that those who are not will soon.
The feature was first spotted by MG Siegler, and has attracted the attention of others throughout the Blogosphere. Some suggest that the feature could eventually be monetized, though this notion was downplayed by Twitter in a conversation with Siegler. As he points out, it is more a user discovery feature, which could increase follower counts substantially.
Name results surface three top names for the search, along with a link to "view all name search results". It shows clearly when an account is verified, and the results will provide the Twitter hovercard feature showing more info, when moused over.
For big names, this means that a verified account may be more crucial. For everyone who cares about being found on Twitter (for business, for example), this seems to indicate that optimizing you profile to be found is more important than ever.
Little is known about how to do this, and those who have less common names stand to have less of an issue with it, but those with more common names are essentially competing for visibility.
Beyond account verification, I would imagine that the "resonance" factors taken into account for promoted tweets would probably factor in here. This is only speculation, but the more active you are on Twitter, the more followers you have, the quality of those followers, and their interactions with your tweets (retweets, replies, favorites, etc.) likely all play their roles.