My Bungie account doesn't register that I own the game on my Blizzard account or something else. If I try to join a clan an error pops up, that says that I need to start the game on my account, but I'm running the game already in the background. In once when I try to reconnect my Blizzard account to my Bungie account an error did pop up, that said, that I'm connected with the other blizzard account, but I only have one blizzard account.
On Bungie.net, please go to your profile settings, go to Accounts & Linking, and insure you have the proper Blizzard Battle.net ID connected to your account. All that's showing up right now is your Playstation account on this profile (if you have others, they may be set to hidden, which you can see in the same section I mentioned above).