@Html.ActionLink("Manage List", "Index", new { @class = "DynamicClassName" });

// Error 
// yes, myChangingColorClass is declared C# valid string 
@Html.ActionLink("Manage List", "Index", new { @class =  @myChangingColorClass });

Best How To :

This can be do by two ways one is by setting value in ViewModel class or by setting value in ViewBag, ViewData or TempData.

Way 1) Preffered way Strongly Typed: Set css class name to viewmodel class attribute:

Class Student
{
  public ID BIGINT {get; set;}
  ... //other properties

}

Class StudentViewModel : Student
{
   public CssClass string {get; set;}
}

//controller action

public ActionResult Index(){
  StudentViewModel objModel; 
  //initialize model

  objModel.CssClass = "myCssClass"; //set css class name to viewmodel 
  return View(objModel);
}

//in view use code like below:

@model namespace.StudentViewModel;
@Html.ActionLink("Manage List", "Index", new { @class =  Model.CssClass })

Way 2) Set css class name to viewbag / viewdata / tempdate. But this is not prefered.

//controller action

public ActionResult Index(){

  ViewBag.CssClass = "myCssClass"; //set css class name to ViewBag
  //or
  ViewData["CssClass"] = "myCssClass"; //set css class name to ViewData
  //or
  TempData["CssClass"] = "myCssClass"; //set css class name to TempData

  return View();
}

//in view use code like below:

@Html.ActionLink("Manage List", "Index", new { @class =  @ViewBag.CssClass })
//Or
@Html.ActionLink("Manage List", "Index", new { @class =  @Convert.toString(ViewData["CssClass"]) })
//Or
@Html.ActionLink("Manage List", "Index", new { @class =  @Convert.toString(TempData["CssClass"]) })

Please let me know, is this works for you?