Hi @danijelcamdzic, do you mean the actual Object Type as listed in the Library? That indeed seems to be limited to the emojis that AnyType supports. For Objects themselves with Layout set to Profile you should be able to upload an image as icon (but there you cannot select an emoji 
)
Edit: linking some related Feature Request:
It seems your specific question (which might be based on a need?) is not yet raised on the forum. Would you be willing to create a feature request for this?