I have a Silverlight application (using MVC) and when i\'m building in visual studio, using Visual Studio Development center, there\'s no problem, the HttpContext.Curr
These might resolve the issue(It did for me). In IIS Express change the project property values, "Anonymous Authentication" and "Windows Authentication". To do this, when project is selected, press F4 and then change these properties.
In case you are deploying it on IIS locally, make sure local machines "Windows Authentication" feature is enabled and "Anonymous Authentication" is disabled.
Refer to
https://grekai.wordpress.com/2011/03/31/httpcontext-current-user-identity-name-is-empty/