Many business owners join Twitter only to find their name or logo and other trademarked-material already being used by someone else on Twitter. This happens to many small business owners on Twitter, another users is already using the desired Twitter handle. Twitter has a dedicated resource page to help you with advice and tips and tricks. Although small business owners are unable to verify their accounts as of now. There are many reasons for that also, some businesses have names that are too common and unless it is trademarked it would be difficult to verify. Twitter have said that they have a way to determine and act when trademark violations are reported. They will check if someone else is using your name with the intent to mislead and confuse others users. If that is established Twitter will move to clear the issue.
What information dies Twitter require if you want to report a trademark violation:
Username of the reported account (e.g., @safety or http://www.twitter.com/safety):
Your company name:
Your company Twitter account (if there is one):
Company website:
Your trademarked word, symbol, etc. (e.g. Twitter):
Trademark registration number:
Trademark registration office (e.g., USPTO):
You are also clearly advised to maintain the accuracy of your Twitter account and clearly mention your company website name, official bio and location.
If however you do want to use the name of a registered company as your Twitter handle you can do so but you need to be clear about the intent in the Bio. If you are a fan page, unofficial account or not affiliated with. This needs to be mentioned clearly.