It's true, it's important to think of the words we use, if we are referring to Conan the Barbarian or any other PD-content. I can strictly speak only of Finnish (EU) law... but..
It's good to note that "concept copyright" does not exist. It's true that the copyright extends further than just the name, but you can't copyright curves, dots, talking rodents, stories where all people are animals with clothes etc. Trademark law concerns the stuff related to the trademark, copyright law is all about the content, and when this interferes with Mickey, it's indeed a can of worms, I can only argue how it should be (I'll do that in next paragraph).
There's absolutely no sense if PD works can be trademarked. Companies would trademark everything that's PD, from Gilgamesh to Shakespeare. You couldn't use any PD works anywhere, ever. If that happens, we need to break that law through means of civil disobedience until the end of time.
Conan the Barbarian (the one in Howard's work) is PD, and isn't trademarked, and can't be trademarked, because it conflicts with copyrights. This is absolutely the case in Finland (EU), but I believe this is also the case internationally. A trademark like "Conan video games" is almost certainly against the law, as there is a significant risk of confusion with Conan the Barbarian, and even if it were accepted, you could still use Robert E. Howard's Conan the Barbarian, but probably should take care on wording (e.g. don't say that this is "Conan video game", but say that OpenMW's example suite is a video game based on Conan the Barbarian). Of course, people can sue you for whatever, but you have to base actions on the principle, that by doing legal stuff you wont be in trouble.
edit: The term "concept copyright" is a bit difficult term, and might be misleading here. What I mean that you can't copyright wider concepts, or general concepts that you have in your work. You can copyright the actual stuff, including visuals, text, etc. but you can't go any wider than that, copyrighting things that "kinda feel like same". There are also different interpretations on this worldwide, making this even more difficult.