$MachineName

$MachineName is a string which gives the assigned name of the computer on which Mathematica is being run, if such a name is defined.

For many classes of computers, $MachineName is the network host name.

$MachineName is "" if no name is defined.

See The Mathematica Book: Section 2.13.5.

See also: $MachineDomain, $System, $MachineID.