For example, I wanted to see if any of my immediate family is on Twitter, so I searched for schwartz. It looks like I am the most popular Schwartz on Twitter (ahem). But it does list another 233 people with the name Schwartz, so I will scan through them to see if I know anyone.
I do wish there was an RSS flavor for this search, so I can track particular names. But the normal Twitter Search has RSS, so that works.