The output image filename created in the arcgisoutput folder for a map service looks similar to the following:
It has an extension of .png, .bmp, .jpg, .tmp, or .gif depending on the type of output file created.
There is no inherent meaning to this filename. The filename is generated to be unique, similar to a Globally Unique Identifier (GUID). However, there is no way to associate the filename to the map service that generated it.
This is slightly different than the output image generated by ArcIMS, where the filename included the mapservice, server name, and a series of numbers in a format such as, <mapservice_<servername>735623000.jpg.