It's almost certain that you don't want those classes to be static. Static classes are shared across the whole app domain so if you update MyName to "John" for UserA then it is also "John" for UserB.
That aside, if you want to update the data from the View then it's just a case of
MyWebApplication.Models.Information.MyName = "XYZ";
If you want to to it via the client browser then you'll need to use ajax. Have a method on a controller that accepts a new name and update the class in that method, then call that method via ajax on the client browser. Google "javascript call mvc action ajax" and you'll find loads of examples of how to do this.