The vast majority of free software projects do not have a registered trademark. In cases where a free software project does have a trademark, distributions usually will rename the package (distributions do have lawyers and they will usually kick up a fuss in cases like this).
The case of the Linux mark is really weird, because basically all distributions are given license to use it but almost everyone still specifies that the trademark is owned by Linus.
(Also my example for GitHub was their fork of git, not Linux.)
Didn’t you mention elsewhere in this thread that Suse and Red Hat patched Docker, not just to backport fixes but to add features which upstream explicitly didn’t want merged? Surely Docker has a registered trademark. So following your reasoning, Suse and Red Hat should have stopped using the Docker trademark. Yet they didn’t. That example seems to contradict your argument that distributions are very careful to respect registered trademarks, while considering unregistered trademarks to be basically a free-for-all.
The case of the Linux mark is really weird, because basically all distributions are given license to use it but almost everyone still specifies that the trademark is owned by Linus.
(Also my example for GitHub was their fork of git, not Linux.)