Samsung stock message app used to display a contact picture bubble as a notification. I could always SEE who was texting me without opening messages. The new update rolled out on my phone yesterday. Totally messed up all notifications and the stock message app now shows an unattractive generic "chat" icon. After hours of trouble-shooting, I contacted Samsung and was told that "this feature changed with the new update." Taking away convenient features is NOT an "improvement"!!
I did get them back after clearing cache and data, removing Samsung Account, and re-adding account. Also, check "allow bubbles" in Developer Options and within Messages you MUST have "preview" toggled on. Not sure why, but when I turn off "preview" the contact pics disappear again and I get generic "chat" icon.