How can I access HttpContext.Current.User.Username from a web application in a WCF service?
Actually, with Asp.Net Compatibility mode on, you can access HttpContext.Current.User from a WCF service hosted in the site. See Microsoft's site for details: https://msdn.microsoft.com/en-us/library/aa702682(v=vs.110).aspx
If your service is hosted in an Asp.net site you just need to update your web.config to set aspNetCompatibilityEnabled="true" on the serviceHostingEnvironment element: