Twitter has recently added a profiles directory where all the public Twitter profiles are listed alphabetically by name. Facebook offers a similar people directory as well that seems to have heavily inspired the design of Twitter’s directory. Google Plus too maintains a public listing of profiles but the information is hidden inside thousands of XML files.
People directories, likes the ones now available on Twitter and Facebook, aren’t necessarily useful to human visitors (unless you are trying to research particular names or surnames) but they are like sitemaps that help search engines bots discover every single profile that exists on the social network.
Twitter’s people directory doesn’t have a search function but you can take the help of Google to find the existence of your name in that massive directory. Try the following search query in Google:
site:twitter.com/i/directory/profiles "your name"
There are 100 Twitter profiles listed per page and Google has discovered about 250,000 pages so far which is equivalent to 25 million profiles. They still have some work to do as Twitter has in excess of 500+ million profiles and most of them are public.
The directory lists both English names as well as profile that have non-Latin characters in their names.