Latest update from my side. I thought I solved the issue via the Apple support but I did not, unfortunately the origin of the issue was not clear. Now, after many test I carried out, I think the issue is that after a whatsapp call or a skype call (to me it happens with skype) when someone calls you again, the iphone shows the caller ID of the last person you called on Whatsapp or Skype.
If you "kill" the app in the background immediately, then the problem looks gone. I called myself from another phone and funny was that on my apple watch it was showing me the right ID caller, while on the iphone it was showing me the last person I called on Skype. When i killed the skype app then I got the right caller ID. So, mine is not a fix, just a work around :(
Anyone with any update on this would be appreciated.