Afaik, it doesn't have a copyright, I mean it's a decentralized cryptocurrency so it's kind of stupid and ironic that bitcoin has a copyright, look around you, there's a lot of bitcoin forks out there that have the code of bitcoin but there's no problem because there's no copyright to bitcoin and no one has registered bitcoin to a patent or trademark office so you are safe with your t-shirt design business.
Satoshi Nakamoto as the creator of Bitcoin is still a mysterious figure whose identity is unknown, so it is impossible for Satoshi Nakamoto to register
Bitcoin in order to have a patent or trademark. Of course this makes Bitcoin does not have a copyright, so if we want to sell t-shirts with the Bitcoin
logo we don't need to ask anyone's permission. Because Bitcoin gives freedom to everyone, to use the Bitcoin logo for anything. Even in some online
stores, there are already many selling t-shirts with the Bitcoin logo, but the online shop has no problem with copyright.