Would be handy to have a class called other-person in the Div with a class of es-convo-messages__item. Attached is a screen shot showing an example of styling one could apply to highlight the difference between you and the person you are communicating with. The slight styling would make it immediately obvious which posts are yours and which one's are the recipients. Many social network sites use a class like this to differentiate this.

And of course if it was just a class added, it would be up to us to decide what styling (if any) to include.