Contact picture not showing when I call others

I set a contact picture in my contacts for myself... basically a pic of a cat.

When I check on a friends phone, it does not show on his phone in any way.. not in the contact for me, not in favorites, not in imessages. Not when I call him. I think it should but not sure.

I'm using an iPhone SE with iOS 12.2. There is no contact photo setting in Settings/Messages.