You're thinking of trademarks. Different body of law.

EDIT: e.g. https://www.mozilla.org/en-US/foundation/trademarks/policy/

You can have copyright open source code, which is what allows open source licenses to enforce their terms. Open source doesn't mean "free to do whatever you want". There are very restrictive open source licenses, and you can deviate from the common open source licenses.

https://en.wikipedia.org/wiki/Software_copyright

Which project copyrighted its name and logo?