WPF ListView DataBinding

Question

PLease i am having a severe problem in WPF listView Databinding. I bound the list view to a list varsList. and assign the item source of the listView to varsList.But when i change items in varsList they are changed in the list view but the display text of the items is not changed. I tried to use INotifyPropertyChanged but it does not work. The code is :

Variable Class:

public class Variable:INotifyPropertyChanged
{
    private string name;
    public string Name
    {
        get { return name; }
        set { name = value; OnPropertyChanged("Name"); }
    }

    private VariableType type;
    internal VariableType Type
    {
        get { return type; }
        set { type = value;  }
    }

    public Variable(string name,VariableType type)
    {
        this.name = name;
        this.type= type;
    }

    public override string ToString()
    {
        return string.Format("{0} ({1})",name,type);
    }

    #region INotifyPropertyChanged Members

    public event PropertyChangedEventHandler PropertyChanged;
    protected void OnPropertyChanged(string propertyName)
    {
        if (PropertyChanged != null)
            PropertyChanged(this, new PropertyChangedEventArgs(propertyName));
    } 
    #endregion
}

private void VariablesController_Loaded(object sender, RoutedEventArgs e)
{
    Binding binding = new Binding(); 
    binding.Source = VariablesTable.Variables;
    //binding.Mode = BindingMode.TwoWay; (gives Error)
    BindingOperations.SetBinding(lstVars, ListView.ItemsSourceProperty, binding);

    if (lstVars.Items.Count != 0)
        lstVars.SelectedIndex = 0;
}

private void btnEdit_Click(object sender, RoutedEventArgs e)
{
    VariablesTable.Variables[0].Name = "Hani";
    //I also tried the below code with out benifit
    /*  BindingExpression ex = lstVars.GetBindingExpression(ListBox.ItemsSourceProperty);
    ex.UpdateSource();
    ex.UpdateTarget();*/
}