Answer
As of ArcIMS 9.0 Service Pack 2, the 'Name' attribute in the WMS service's Capabilities file corresponds with the LAYER element's 'id' attribute in the configuration AXL file of the WMS map service.
The WMS 'Title' corresponds with the ArcXML 'LAYER element's 'name' attribute.
Prior to this version, the Capabilities file's 'Name' attribute was used to refer to the LAYER element's 'name' attribute.