I have Swiftkey as my keyboard and it allows you to add emoji's to the contact name. You first have to enable the emoji feature. Once you have installed the Swiftkey keyboard open your contacts and select one you would like to change. Click on the little pencil to edit the contact, then click in the contact name section to bring up the keyboard. The lower left key with the 123 has the settings for the keyboard if you long press it. Go to settings then layout and check the last one that says Enter Key long press for emoji. back out to your keyboard and you can long press on the enter key (bottom right) and it will bring up a whole bunch of emojis.
I hope this makes sense. Let me know if you have any questions.