Compared to other social networks like Facebook and Google Plus, Twitter's name requirements are fairly lax. You don't need to provide a real name, so you can go by almost any identity you want. Even parodies of companies and celebrities are fair game, provided you don't claim to represent the person or group in question. However you want to use Twitter, the best names on Twitter are short and clearly identify you to help people find you -- whether by your real name, an online pseudonym or your company name.
Twitter only places a few restrictions on its usernames. Most notably, a username must have 15 or fewer characters and contain no symbols other than underscores. Finally, usernames can't contain the words "admin" or "Twitter," which are used to help distinguish official Twitter accounts.
Twitter doesn't provide any way to claim a name that's already in use, even if the user is inactive. To take another user's name, that user would have to voluntarily change his name first, or delete his account. The only possible exception is if you want a name tied to a trademark that you own.
Names for Personal Accounts
When picking a name for your personal Twitter profile, start by deciding whether you want to use your real name or not. If you plan to interact mostly with real-life friends or to represent your company, a real name provides clarity and professionalism. Even if you don't use your real name as your username, you can still display it in the Full Name section of your profile.
If you'd rather use a pseudonym, think about whether you want your Twitter posts tied to your other online activity before automatically writing in the same handle you use across the Web. There's nothing stopping you from creating a completely new persona for use on Twitter alone. Just don't pick a name that you wouldn't want friends and coworkers to hear, unless you plan to completely avoid your real-life acquaintances on the site. Every user must have a unique username, so if the name you want is already taken, add underscores or numbers to find a similar available handle.
Names for Business Accounts
The biggest challenge for picking a Twitter name for your company is keeping it brief. Even if your entire company name fits in under the 15-character limit, it might not be the best choice -- longer Twitter names are harder for people to remember, harder to type on phones and leave less space per message for people who contact you. You also shouldn't add random underscores or numbers to a company Twitter handle, as they make it harder for customers to find you.
Instead, stick to common-sense shortenings of your business name: drop the "Inc," "Corp" or "LLC," and use abbreviations when possible. Just make sure that any acronyms or initializations you use don't have an unintended interpretation.
Where to Enter a Name
If you want to change your handle later, click your profile picture on the menu bar and choose "Settings." Enter a new username and press "Save Changes." Changing your username won't affect your account -- you keep your followers, lists and other settings -- but you should post an update about your new name so that your followers recognize your new handle.
As of publication, Twitter does not offer name changes through its mobile apps -- only through its website.