I too am having this issue. I have confirmed that:
1) The contact details in the Contact app address cards do not overlap
2) It is not a group chat.
It looks like the Messages app thinks it is a group chat, but it is not
In the Mac Messages app:
1) In the left hand conversation summary window the contact icon is for Contact #1 but the name displayed is for Contact #2
2) In the main conversation detail windows, I see both "iMessage with <phone #1>" and "iMessage with <phone #2>". All incoming iMessages from Contact #1 and Contact #2 are displayed in the conversation. It looks like a group chat, but it is not.
3) Any outgoing iMessages I send in the conversation only go to Contact #2.
On my iPhone:
1) All iMessages to / from Contact #1 and Contact #2 are displayed properly on my iPhone (i.e. they are separate individual conversations). But in the Mac Messages app, some (not all - not sure what the trigger is) messages to / from Contact #1 show up and all messages to/from Contact #2 show up in the same conversation.
So it looks like the Messages app is somehow confused. Appreciate any ideas for solving this issue. Thanks.