A hypothetical -- but certainly possible -- scenario: $distro (e.g. Debian, RHEL, Ubuntu) takes the Caddy source, removes the controversial header, builds a binary package, and distributes it as "caddy" via their standard repositories. Light Code Labs doesn't approve of this and asks/demands that $distro stop using the trademark. $distro now has to make a choice: remove the "unapproved" changes from their package, stop distributing their package, or rebrand the software under a different name.
(That potentially could have happened here [2,3] but it was quickly resolved well before it got to that point.)
I don't think "it doesn't" is correct -- at least not for 100% of cases.
[0]: https://en.m.wikipedia.org/wiki/Mozilla_software_rebranded_b...
[1]: https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=354622