There's a Twitter account that has our company name, but it hasn't been used for a decade, and has only one Tweet. I'd love to pay Twitter to talk to them, so we can take over the account. Maybe they have a process for this anyways? I don't know. All I know is this account gets tagged all the time by people trying to tag our company.
Find your way to your local Twitter ad rep. They may be able to facilitate transfer of an inactive handle. It obviously helps if you are buying or intend to buy ads on Twitter.