Is on Mac OS X any way to hide my hostname?
If I go to check to some web services my IP, so there is displayed yet the hostname. I would like to hide that.
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The operating system has no control over this.
Your hostname is retrieved by a remote Web server via reverse DNS lookup of your IP address. If you control the IN-ADDR.ARPA domain that covers your IP address then you can have the reverse lookup return anything you like. Otherwise, it is out of your hands. In any event Mac OS X has no control over it.
Some Internet protocols demand host identification directly. For example, SMTP servers expect clients to identify themselves with the HELO or EHLO directives. Changing the local hostname usually changes what an SMTP client sends to a server as host identification, but this behavior is specific to mail client software and its configuration. Even so, the remote server can (and usually will) do a reverse DNS lookup in addition for logging purposes.