Copyright issue

[squarebear]

Say for example, I wrote an internet game called "ABC", put it online and let people play it for free. Eventually it became popular and unknown to me, people copied it and put it on their own websites. I find this out after several months that there are at least 1,000 sites with my game.

One day, I receive a letter from a company saying they own the trademarked name "ABC" and they want me to rename the game. This I do straight away and apologise, as I didn't realise "ABC" was copyrighted but naturally I cannot remove it from other websites but my own.

What are they likely to do? Blame me for making the game? Or go after the other websites? Or something else?

[Gmcd01]

To begin with, a distinction must be drawn between a Trademark (TM) and copyright. A trademark is only (prima facie) valid if on the TM register, and can only be used against the class of products for which it was registered (e.g.: cars). Thus, there is a chance that your game would not infringe a 'competitor's' TM as they would not have it registered for use in the class of "computer games". Further, you are probably not using it "in the course of trade" (although nothing is ever certain) and I would advise that you would likely not be infringing a TM.
If the TM is not registered (so that instead of a (r) after the word, you see TM), you may be infringing on a competitor's "goodwill". Passing off is a common law action for people who are using words as Trademarks, but for whatever reason haven't (or couldn't) register them. This is an action that effectively prevents one from passing off their goods as those of another trader's. However, this is really a side issue to your question.
In the U.K., it is HIGHLY unlikely that the word ABC would be copyrightable. I recognise that this question might be hypothetical, but in the U.K. the courts are very wary about granting copyright protection over short words or phrases. This would have the effect of "locking up" everyday words and phrases that the ordinary man needs to use in his life. However, if we pretend that ABC is for some reason copyrighted, then it is very likely you have infringed the copyright by reproducing a substantial part of an original work that you had access to.
The copyright holder would probably sue you for inringement, and force you to change the name. Once that had been done, they would then contact each of the website admins in turn, informing them of their legally exclusive right to the name, pointing out the successful recent action against you and requesting that the content be removed/renamed as you have renamed it. If the websites f

[Gmcd01]

.... If the websites fail to do this, I would imagine that the company would then send increasingly threatening letters, potentially culminating in a lawsuit. Further, if refusal to co-operate is widespread, the company could seek an injunction, prohibiting any new hosting of the copyrighted material.
This would be PR suicide in the real world of course. Many companies make millions from such widespread use of software too- Microsoft opened up their programs where Apple chose not to- and who's the global brand now? This scenario is slightly different from ones where the content itself (rather than just a name) is 'stolen'- in those cases, ISPs can be made aware of the problem, who are then legally obliged to remove such content within a 'reasonable' period of time.
Hope that answers your question (and many more besides!)

[squarebear]

Thank you for your super answer. That certainly is helpful