Particularly just the shipping names related to the pairing of Betty and Jughead aka Bughead and Bethead (lord, pick better names). They filed trademarks on both names, and they're pending at the moment.
In order to keep the trademark, they'll have to use it in canon so expect Cheryl to drop another set of hashtags on the show. Or merchandise. Or even more noteworthy, the comics but in that case it would probably be the main Archie comics line rather than the Jughead line which is the only iteration where Jughead is asexual.
It seems doubtful at this time that they'd trademark any of the shipping names for f/f or m/m pairings. It also remains to be seen if they'd C&D fans or fanfic writers like how fanfiction for Archie comics wasn't allowed on FFN (and still isn't though there is a section for Riverdale) or how the current showrunner of Riverdale once had his college amateur play shut down by the old Archie Comics guard for portraying Archie as being gay (the play also featured time traveling Archie who interacted with celebrity kidnappers and working for Pixar).
what would you trademark for shits and giggles if you could?