Perhaps others have encountered the same problem. It seems the default class name for a WCF client proxy is Service1Client. When I delete the service reference and recreate it the name keeps coming up the same. (Although it does give me the opportunity to name the namespace.)
When I chose Refactor/Rename on Service1Client (ie: the class name for the proxy), it fails with the following message:
The file 'Service References\myNameSpace\References.cs' could not be refactored. The current object is autogenerated by the Wcf Client Generator and cannot be renamed.