What info about me do my FaceTime contacts see?

Do they just see the email address or phone number that I'm using as caller ID? Or do they see my name (which is asscociated with my Apple ID)?

Can they see any other info about me?

Can any of this be contolled by me, i.e. what info they see?

For comparison, with Skype I can click on a contact's name and see their Profile with lots of info about them, depending on what they have included. This might be name, location, a photo, birthday, etc.

Thanks!