What info does a Mac broadcast and how to hide it? I want to run a Mac in the cloud as a webserver and for facilitative use. I've secured most of my used tools already, but I was wondering about the OS itself.

Imagine I'm running an up-to-date Yosemite. How could I check what information a third party could obtain from the device. If information could be found, how to hide it?

I noticed some SSH services on Linux servers bluntly giving their exact OS version until the release number. I would want to prevent stuff like that being broadcasted and just wanted to double-check if OS X would broadcast such and how to obfuscate it or hide it fully. I can understand I can't hide my server is running OS X, but I would at least not like the external party to know more details if they were broadcasted.
First make sure that you're running a firewall that is prohibiting all inbound and outbound connections on the server. Then open only those ports you need for the production to run fine.

Most applications can be configured to not identify their exact version, but remember that this is not really giving you any more security, it is just a tad harder to exploit.

After you've "hardened" your machine like this you could fire up a second machine in the same subnet and launch a utility like Wireshark (Wireshark download page) to listen to the chatter of your cloud server. This way you get additional hints about processes that you might want to silence.