What is the client representation of server objects called?

Question

I've got an object that is running on the server:

class Foo {
    List<string> whatever;
}

This object is mirrored on clients using some transportation method:

class ClientFoo {
    List<string> whatever; // synced to server
}

How is such a client library usually called? I thought about ClientEndpoint, ClientLibrary, LocalObjects, ... but nothing really seems to describe it.