iMessage does not work on my mac

I have big issues with imessage. On my Mac Im not able to send to certain phone numbers even though I know they are on iMessage. I try the same on my phone and It works fine.

Doing it on my Mac I get the message saying the phone number xxxxxxxx is not registered for iMessage. For other contatcts/numbers it works fine.

If I send to the same phone number from my iphone the Mac versjon of iMessage display only the phone number and not contact name even though the contact lists on both phone and Mac are identical.