After updating my iPhone and iPad to latest 15.3 iMessages is not syncing between my devices

I recently bought a iPad and I enjoyed the iMessage sync when I’m in different rooms and it was so convenient. But apparently I stopped to sync between devices and sometimes even my existing contacts name is not displayed in my iPhone when they call. I see only numbers. I tried to ensure all the possible settings but i’m not sure how to resolve it. Could you please give a resolution to this regard? Please don’t give lame advice by repeating what I already did like checking through settings in iPhone and iPad also logging out and logging in in etc. need a technical solution to overcome the glitch not diagnosis.