Twitter requires users to provide the real name and username. Real name is the name where you want others to identify you online while username is the name that appears at the end of your Twitter URL.
In sending SMS commands and 3rd party applications, twitter uses your real name. Your username is used when people try to send an @reply or direct message on your twitter account. The use of real name allows people to recognize you. Twitter allows users to type in real names up to 20 characters and username name up to 15 characters. The use of spaces in the username is not allowed but it may contain numbers or letters and the ‘_’ sign. Your full name or real name is shown on your sidebar profile. When the WHOIS command is used, your full name is shown as results.
Changing Twitter names.
You can change your twitter real name or username anytime under the settings page twitter.com/account/settings. Such changes will not affect your existing updates, @replies, direct messages, or other data. However, change of your username will change your Twitter URL, thus, it is best to let your followers know of your change in username in that way they will not send an @reply or direct message using your old username. As soon as your user name is changed, all @replies and links on the former user name are no longer valid.
It is also important that you secure your Twitter name, as there may be "unauthorized" individuals who are twittering within the community at your expense.