How to competently design a database so that the global object has some properties rewritten?

Question

PHP

It so happened that each client of our application has its own database. Complex enterprise application.
There are some types of objects - which are the same on all instances. One simple example is countries.
So the question is how to organize the sharing of such objects between different sites. And what's more - some objects still have local customization - some fields are different. For example, one client asked to name the country not USA but US.
The example with countries is only the simplest, there are more complex objects, and there are more customizations in them.
How to organize it all? The database type can be any MySQL, MongoDB, PostgreSQL, etc. The choice is not limited.