Chromium in debian is extensively patched. It disables third party cookies, for example.
That said, I couldn't find a real trademark policy page for Chromium. If it's the generic Google one: http://www.google.com/permissions/trademark/our-trademarks.h... then Debian is clearly in violation of it.
Debian does apply patches -- just look at their packaging repository:
http://anonscm.debian.org/cgit/pkg-chromium/pkg-chromium.git...
Google also documents that Chromium may have distro-specific patches applied and how it differs from the Google Chrome binaries provided by Google:
https://code.google.com/p/chromium/wiki/LinuxChromiumPackage...
https://code.google.com/p/chromium/wiki/ChromiumBrowserVsGoo...
Mozilla lets you use Firefox if you don't change the source; I believe Fedora and other distros release it with the original name. The difference is that, unlike Debian, they don't apply patches to the upstream source in their builds.
And I find it hard to believe that Google allows you to use the Chromium mark if you release a patched build; they're probably no different than Mozilla in that regard.