I was just trying to find a certain Private-Conversation in my Inbox.
It took some time to look for this, as the subject-title of most of my messages are very similar.
Also at most of those, my own Avatar is showing-up - as I assume it is always showing the Avatar of the person who started a specific Conversation.
As I have started most of the Conversations, it is showing my own Avatar on most of my Inbox, which does not help to find a specific Conversation.
BTW: looking onto the Inbox-Drop-Down, it is also showing my own Avatar. It does not help to see my own Avatar there, it would help in a big way to see the avatars of the users who are talking with myself.
For the Inbox-Drop-Down-box, I would suggest to show the avatars of people who I am talking with, but not show the Avatar of myself (just because I had initiated the Personal conversations).
For the Inbox-list, I would suggest you show the Avatars of ALL people who participated in a certain conversation.