As far as I know there's no official channel for this.
I've had some success in the past tracking down the owner by checking previous messages, followers, and who they interacted with. Googling names, checking Facebook, etc. But it depends on the account and level of activity on whether that's a feasible strategy.
If you know the right people at Twitter, they could obviously help as well but I'm assuming you don't have such contacts. Me neither, for that matter.
Some people might suggest registering a trademark and reporting the account as infringing on it. I don't know if anyone ever made that work though. As the infringement only counts when there's reasonable doubt about whether represent your brand which is a hard case to make for an inactive account.
It doesn't hurt contacting support, but I don't know of anyone succeeding that way either.
My advice: try to do some research on their followers/activity and if that's fruitless move on and try again once your company is more established. By that time it might be more likely Twitter will care.
I know I'm a little late to the party, but I found a decent post on this a while back (josephliu.co/twitter-username-taken). It goes along with what Marc was saying about reporting the account:
I've never tried it myself, but some people in the comments are saying it worked for them. I'd love if they would purge inactive accounts every few years and release the usernames!
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