on click store your dropdownlist selected text in session
protected void btn_Click(object sender, EventArgs e)
{
Session["abc"] = dropdownName.Selected.Text;
}
check session variable and assign session stored value in label
protected void Page_Load(object sender, EventArgs e)
{
if (Session["abc"] != null)
{
lblShow.Text = Session["abc"].ToString();
}
}
Use Master Page that best suitable for this kind of situation