We've covered how weird the copyright for this stuff works (see my entry for Blue Beetle), but for most of this series, I've stuck to heroes that are very much safe to use (even Blue Beetle has seen a comfortable amount of non-DC comics and movies for me to mention them). Today's hero is someone who you definitely can't use.
Billy Batson was just your average boy/radio presenter when, one day, he - no, wait, why am I explaining their backstory, they're Captain Marvel/Shazam, they have a big movie about them and they're a relatively well-known DC character, I don't think I need to explain them that much.
Now, Captain Marvel was originally published by Fawcett under loads of different comic lines, all of which you can just easily find online in a legal way since they are just public domain. As I mentioned earlier, most of the heroes covered here fall into the public domain do so because their copyrights weren't registered or renewed between the late 1920s and early 1970s (do your own research). Now, Fawcett was great at trademarking their comics, but really blew it when it came to registering/renewing copyright, hence why this guy is in the public domain (along with some of their other characters, like Peacemaker).
So, what are the trademarks? Well, obviously Shazam is off the table since that was entirely DC's idea... Captain Marvel can't be used since Marvel Comics now owns that one for their own character... and oh, you can't use the name "Billy Batson" either, since DC also owns that one... basically, if you want to use this character, it has to be a nameless cameo or an expy (the latter of which you could already do with any copyrighted character).
In short: just don't bother.