Just noticed this feature while using the Android Facebook app – you can apparently name conversations, what the hell.
To name a conversation:
Tap on the information icon (the top right icon that looks like an “i”) when viewing messages on the app. A new screen appears. This screen allows you to name the conversation, add an image, add participants or leave the conversation.
I had a closer look at the web application, and while I’m not 100% sure, I’m reasonably sure this function is either masterfully hidden or entirely non-existent.