Talking about patent registration on logos, as far as I know, Bitcoin Logo is released under a public domain license, meaning that it is free to use*.
https://bitcointalk.org/index.php?topic=1756.0
https://commons.wikimedia.org/wiki/File:Bitcoin_logo.svg


https://cri.dev/posts/2021-02-17-Bitcoin-trademark/

* Although some are trying to patent Bitcoin (logo and name), for example, in Spain: https://www.tmdn.org/tmview/#/tmview/detail/ES500000004046141