When you receive an iMessage from an unknown party, how does Messages identify that person for you if they’re not already in your contacts? Apple has a backchannel in its proprietary multimedia texting system that transmits your name and image to the recipient based on settings you can control.
In iOS/iPadOS, go to Settings > Messages > Share Name and Photo; in macOS, open Messages and go to Messages > Preferences > General (Monterey and earlier) or Messages > Settings > General (Ventura or later).
You can start by enabling or disabling sharing your name and profile image: use the Name and Photo Sharing switch in iOS/iPadOS and the Share Name and Photo checkbox in macOS. When disabled, these items aren’t shared with people you message for the first time; anyone who previously received them and stored them will retain that information.
Read more at Macworld.com