Changing Label's Text

Go to property and Set the AutoPostBack property to true for the radiobuttonlist.

and try out the following code:

protected void Page_Load(object sender, EventArgs e)
    {

        if (!IsPostBack)
        {
            //check the first item of radio button list on first time of page load.
            RadioButtonList1.SelectedIndex = 0;
            Label1.Text = RadioButtonList1.SelectedItem.Text.ToString();
        }
        else
        {
            Label1.Text = RadioButtonList1.SelectedItem.Text.ToString();
        }
    }

Note: You also can do it by using java script.

Edit: Oh sorry, Ryan replied already while I am sending the post.