I wish to add our son's Android to my Apple Music Family Plan. His name doesn't appear in my settings screen.

Hello ATL-528.

Thank you for using Apple Support Communities. If your son has their own Apple ID, you can send them an invite via email. The following resources and steps can guide you: Add or remove members from your Family Sharing group on iPhone - Apple Support

On your iPhone:

1.) Go to Settings > [your name] > Family Sharing, then tap Add Member.

2.) Tap Invite People and select Mail.

Once your son receives that email invite, they can follow these steps here: Use Family Sharing with Apple Music on Android - Apple Support

Accept an invitation:

1.) Download the Apple Music app from Google Play to your Android device.

2.) Open your Android device, open the email invitation to join Family Sharing.

3.) Tap the link in the email invitation.

4.) In the "Open with" scree, tap Apple Music.

5.) Tap Accept.

6.) Sign in with your Apple ID and password.

We hope this information is helpful. Cheers.