<asp:DropDownList ID="userDropDown" runat="server" DataTextField="CustomerName"  DataValueField="CustomerId">
</asp:DropDownList>

protected void Button1_Click(object sender, EventArgs e)
{
if(!page.isPostBack)
{
    userDropDown.DataSource = CC.GetCustomers();
    userDropDown.DataBind();
}
}

protected void Page_Load(object sender, EventArgs e)
{
   if (!Page.IsPostBack)
   {
     //bind your datasource here (something like below)
     userDropDown.DataSource = GetCustomers();
     userDropDown.DataBind();
   }
}