My profile picture on iMessages is not appearing for other people on my contacts

Good afternoon borna80,

Welcome to the Apple Support Communities!

I understand you are trying the new feature in iOS 13 to share your profile picture and name in the Messages app.

Have you updated your iPhone to iOS 13.1.3? Has the person you are sending an iMessage to updated their device as well? This feature is initiated when you send a contact a new iMessage and the receiving party manually selects the option to "Update Contact" when prompted in a banner.

Try testing this with a contact who has updated his/her iPhone. Change the photo on your device, and change the option from "Share Automatically" to "Always Ask." Then send a new iMessage to your contact and let us know if this person receives the banner prompting them to update your information on their device.

Let us know the results of this test and I'll do my best to help you with this!

Send and receive text messages on iPhone - iPhone User Guide - iOS 13

"Edit your Messages name and photo

In Messages you can share your name and photo with contacts when you start or respond to a new Messages conversation. You can use an Animoji, Memoji, or custom image for your photo.

Open Messages, tap , tap Edit Name and Photo, then do any of the following:

• Change your profile image: Tap Edit, then choose an option.
• Change your name: Tap the text fields where your name appears.
• Turn sharing on or off: Tap the button next to Name and Photo Sharing (green indicates that it’s on).
• Change who can see your profile: Tap an option below Share Automatically (Name and Photo Sharing must be turned on).

You can also use the name and photo in your Messages profile for your Apple ID and Contacts name and photo."

Take care.