we get these kind of questions almost everyday. so the problem is that there are millions and more apps that is in the play store. you can a million or so more if you factoring in that websites can send you notifications as well......so unless it is something well known, most of these threads never truly get a complete answer.
truly the easiest way is to look directly on the phone. but in most of these types of threads, the phone is not available for one reason or the other.
on that note if you are talking about the icon on the right. it looks like some kind of messaging app or something similar to skype or facetime.