The domain forms part of the username so I don't think any of the methods/properties return what you need. Can you not just do:
var userName = User.Identity.Name.Split('\\')[1];
Not ideal but simple enough. If you want to keep it nicely hidden away you could create an extension method on IIdentity.
The VB equivalent is (where UserWindowsName could be a variable or control used to display the Windows User Name):
Dim userName As WindowsIdentity = HttpContext.Current.Request.LogonUserIdentity
UserWindowsName = userName.Name.Split("\"c)(1)