Whether a competitor has intentionally taken your brand name, or an account which has been inactive for some time is using that name, there are ways to take ownership of it. Twitter’s user policy allows people to reclaim inactive accounts that have been inactive, not been tweeted from or been logged into in several months. Alternatively, if you own the domain name (.com) associated to that brand, you may be able to reclaim that name.

For example, suppose you own omnisity.com and want the Twitter username to match; if it's in use, there's a good chance you can file an impersonation claim and take ownership of the @omnisity username.