Displaying profile photo on others' phone when called
You can not do that. It is not possible to set a profile photo for yourself on other phones. Phone calls transmit nothing but your voice and phone number. You can not transmit a profile picture through a phone call. Third-party apps like Google Hangouts do not use phone lines, instead, they use data, so they use a custom protocol that allows them to send the profile pic of the caller.
The receiver of the call must set a profile photo for you. This must be done for everyone that you want to see the profile photo of:

For iPhone users: http://osxdaily.com/2015/11/07/assign-photo-to-iphone-contact/
For Android users: http://www.howtogeek.com/259513/how-to-change-contact-pictures-in-android/.

They will want to follow the instructions to add a photo to your contact, not theirs.