You cannot set the current application domain.
The AppDomain.FriendlyName property by default has the value of the application file name (Read the remarks section). You cannot change this in the default application domain.
What you can change is the name of your executable assembly. You can change it from your project's properties. Then you can use it like this:
Assembly.GetEntryAssembly().GetName().Name
which always returns the name of the process executable assembly.