Hello andrejagovski,
Thanks for using the Apple Support Communities. We understand you are encountering some issues with the Messages app on your MacBook Pro. We are happy to help provide some guidance.
To begin, we want to make sure that your Mac is logged in to your Apple ID and has a good internet connection. If you choose the Apple menu () > System Preferences, do you see a button to Sign In, or does it show the correct Apple ID there?
Sign in with your Apple ID
Once we've confirmed you have a good working internet connection and you are signed in with your Apple ID on the Mac, take a look at the steps listed in the following article to get signed in to iMessage:
Use Messages with your Mac
If the issues persist, we advise going over the sections in the following article to check to ensure there aren't any outages, that the time and date are set correctly and your software is up to date as well as trying to boot your Mac in to safe mode:
If you can't sign in to your iMessage account or FaceTime on your Mac
How to use safe mode on your Mac
Keep us updated on how it goes or if you have any questions. We hope this information helps.
Best Regards.