Traveling internationally SIM card problems

I currently have an eSIM for my iPhone, and when I travel internationally I buy a SIM card from the country I’m in. When I insert the new SIM in my phone I have problems with my contacts and iMessages. So when I receive iMessages it shows and just the number and not the contact on my phone and as a new message. So I have to manually re-add my contacts number in again on my phone because if I don’t do so I won’t get the message from the contacts and it will only show as their number and not their names. Also when I get back I have to redo the numbers again under my contacts because it will still show as the phone number and not the contact. Is there anyway to resolve this issue where I just get the messages and not have to redo my contacts again and get separate iMessages?