Hey there Janlapke,
It sounds like you are unable to sign into your Apple ID in the Messages app. I want to recommend the troubleshooting outlined in this article named:
FaceTime, Game Center, Messages: Troubleshooting sign in issues
- Ensure that you have an active Internet connection.
- Verify that you are using a valid Apple ID at appleid.apple.com. You can also create an Apple ID or reset your password from this website. Other things you should confirm while logged into appleid.apple.com:
- Confirm that the email addresse(s) for your Apple ID has been verified.
- Check for miss-types of the email address
- Check the spelling of the email address
- Check that all letters are lower case
- Make sure that special characters are correct, e.g. no commas (,) where there is supposed to be full stops (.), etc.
- Note You may experience issues if your email address is associated with more than one Apple ID. If you have multiple Apple IDs, log in to appleid.apple.com with each Apple ID and confirm that each email address you wish to use for FaceTime or Messages is associated with only a single Apple ID.
- Make sure the date, time, and time zone are set correctly in Data & Time preferences, in System Preferences.Tip: Enable "Set date and time automatically" in Date & Time preferences to automatically keep this information accurate.
- If third-party firewall or port filtering software is installed, it needs to be configured to allow connections toapple.com, verisign.com and verisign.net. A list of ports required for using FaceTime and Messages is in Using FaceTime and iMessage behind a firewall. Please consult this article for further help configuring firewalls and Internet security software.
- If your /private/etc/hosts file has been modified, make sure that it is not interfering with communications toapple.com, verisign.com or verisign.net servers. Note: Some third-party software installers may modify the /private/etc/hosts file without alerting you. Instructions about how to check and resolve issues with a /private/etc/hosts file are in the "Blocked by configuration: (Mac OS X/Windows)" section of iTunes: Advanced iTunes Store troubleshooting.
Thank you for using Apple Support Communities.
All the very best,