You can use the EnvironmentVariableFetcher, using the environment variable COMPUTERNAME. You can also do this from PythonCreator or PythonCaller using the code below.

import fmeobjects,socket


class FeatureCreator(object):
    """Template Class Interface:
    When using this class, make sure its name is set as the value of the 'Class
    to Process Features' transformer parameter.
    """

    def __init__(self):
        """Base constructor for class members."""
        pass

    def input(self, feature):
        """This method is called once by FME to create FME Feature(s).
        A created Feature is emitted through the self.pyoutput() method.
        Any number of Features can be created and emitted by this method.

        :param fmeobjects.FMEFeature feature: Dummy FME Feature passed in by
            FME. It can be ignored.
        """
        newFeature = fmeobjects.FMEFeature()
        newFeature.setAttribute('hostname',socket.gethostname())
        self.pyoutput(newFeature)

    def close(self):
        """This method is called at the end of the class."""
        pass