That's what happens when 2 accounts are merged.
You have a couple of options. The controls for conversations are located at the bottom of the screen after you check the box on a conversation in your inbox. You can then select "All" (which is just those conversations on that page). Leave Conversation is the equivalent of deleting it. Repeat as necessary.
Or.... There's a nuclear option. And when I say nuclear, there's no turning back from it when implemented. Every single conversation in your Inbox will disappear. And there's no undo once I activate that option.