Unable to change Apple Account number on my iPhone

Check iMessage and FaceTime settings for your device. On an iPhone or iPad go to Settings > Messages > Send & Receive, and make sure both your telephone number and Apple ID are input there and both show a checkmark. If you need more help, check out this link: Add or remove your phone number in Messages or FaceTime --> Add or remove your phone number in Messages or FaceTime - Apple Support

Check your Siri settings to make sure your correct contact information is selected. You can do this by going to Settings > Siri & Search, and making sure that My Information shows your contact card information. If not, tap on it and select your correct contact card information from Contacts. See also: Tell Siri about yourself on iPhone - Apple Support. Tell Siri about yourself on iPhone - Apple Support

Ref. family sharing confusion - Apple Community

To edit your list of trusted items go to the section: About trusted phone numbers and trusted devices in the document Two-factor authentication for Apple Account - Apple Support

To see, add, or change your trusted phone numbers:

- On your iPhone, iPad, or iPod touch: Go to Settings > your name > Password & Security. Next to Trusted Phone Number, tap Edit.

- On a Mac: Choose Apple menu  > System Settings (or System Preferences), then click your name (or Apple ID). Click Password & Security, then add or remove a trusted phone number.

- In a web browser: Go to the Account Security section of https://account.apple.com

If an app or feature on your device is not working, not appearing, or is restricted (grayed out), a frequent reason is it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution.

- Read this support article If your Apple ID or other options are greyed out in Settings —> If your Apple Account is grayed out in Settings - Apple Support

Tap your Settings app > Screen Time > Content & Privacy Restrictions > scroll to Allow Changes and turn on.

- If the device is managed (Settings > General > VPN & Device Management), contact the IT department that is doing the managing.

If you are trying to change your actual carrier phone number …

… you’ll need to contact your carrier for assistance.

Otherwise, your carrier phone number is “set” into your Apple Account at Settings -> Apple Account [Name] -> Sign-In & Security.