Domain for servers, which one you would choose?

Hello there, I have a site which uses a .com domain, and I want to contract a server for its external services.

I don't know what domain I have to use.

Supposing my domain is: google.com, is it better to use google.net or googleservers.com?

Thanks in advance.

Yes, I think that too, but in this case I will not use this as public domain but as internal support.