Unfortunately there is simply no direct equivalent to this VB.NET feature in C#. There is no way in C# to implement an interface method and give it a different name. This can be simulated though by just creating the name you want and having the interface implementation forward to that method name
class WebServiceClass : Interface1, Interface2
{
public string Method1(int result) { ... }
public void Method2(long id, int p3) { ... }
public void Method3(long in) { ... }
string Interface1.Method1(int result) { return Method1(result); }
void Interface1.Method2(long id, int p3) { Method2(id, p3); }
string Interface2.Method1(int result) { return Method1(result); }
void Interface2.Method2(long in) { Method3(in); }
}