In commit e1a9ebdc, "service Greeting {" was renamed to "service Greeter {" and method "rpc hello" was renamed to "rpc sayHello" (and later on to "rpc SayHello").
This fixes some old references to Greeting service and hello method to use the current Greeter service and SayHello method.
I've also tried to improve consistency in the wording/styling around "Greeter service".

the documentation is kinda the most important part so let's put the important things first.

Fixed link the authentication information.