Apple ID error during activation.

Got it, help_me_please2251,

We'd like to have you go to the Apple () menu > System Preferences, then click Date & Time and select “Set date and time automatically”. Click Time Zone and make sure that the settings are correct. 

Which macOS version are you running currently? You can go to the Apple () menu > About This Mac > Overview to check.

Have you restarted your Mac since you've noticed this happening? If not, let's go ahead and restart as well. You can go to the Apple () menu > Restart.

Do you also experience the same behavior if you activate FaceTime in a new user account?

To create a new user account, you can go to the Apple menu  > System Preferences, then click Users & Groups.

Click the lock icon, then enter an administrator name and password.

Click the add button (+) below the list of users.

Complete the fields shown for an Administrator account, then click Create Account (or OK).

Once you’ve created the new account, go to the Apple menu  > Log Out, then log in with the new account and sign into FaceTime to test.

Best regards.

Thanks for letting us know, help_me_please2251,

It sounds like you wren't able to activate iMessage or FaceTime but they're both activated now and your FaceTime contacts are displaying "Unknown" instead of the contact name and phone number, correct?

Are your contacts in Messages displaying as you'd expect?

Are you still seeing an alert within FaceTime? If so, what does the complete message say? Do you see the alert when you're attempting to make a call or when you receive a call or does it happen when you launch the app?

Kind regards.

Hi help_me_please2251, 

Thanks for contacting the Apple Support Communities!

We understand that you're seeing an error when you enter your

Apple ID. Can you tell us what the specific alert is?

Where are you attempting to sign in specifically? Any specific

details you can provide for us will help us to isolate this behavior further.

We look forward to your reply.

Cheers!