I had a similar idea for financing Open Source software projects. The contributing sponsors would get their URL and add-text into a comment at the top of the source-code. The bigger your sponsorship the higher up in the list your company will be. The adds would of course be targeted at hackers, such as come work for us, since only hackers read source-code. So it would be a very targeted ad (like the http-header thing…
Don't do it. People will hate you for it... and never, ever let you live it down. :-/
Credits pages in software, accessible from the main UI, used to be very common, and having names there -- or embedded in source code -- doesn't violate a user expectation.
Server software sending 'Server:' headers also doesn't violate user expectation, though some people prefer to turn these off.
Custom headers that cannot be turned off have a higher likelihood of violating user expectation.
To the OP: in open source projects, some users will attempt to remove undesired behavior, within the rights afforded by the license, but these exercises of copyright can interact adversely with trademarks and other brand protections, and with the surrounding (human) infrastructure and information-space around a project (e.g. names, URLs, references to services, secrets).
Your attempts to reconcile such a situation are nontrivial, and both inaction and action have a high likelihood of resulting in bad press (e.g. user confusion about fork, or heavy-handed enforcement). The harm will persist long after the original situation has been resolved or mitigated.