How do I add Genmoji to contact profile on iPhone?

Im unable see option to add genmoji to contact profile since there are only options i can see is photo , memoji , monogram . Since i want to make recent call list and i message look good so i want to add genmojis ive created using their personalities to their contact photo. But now i cant

[Re-Titled by Moderator]

Original Title: unable to add genmoji to contact profile simce there are only options i can see like photos , memoji , monogram