How to fill a textbox with a MySQL LIKE?

I'm trying to fill in the textbox, when the client is typing the initials of their name, the select goes into the bank and tries to fetch the information. However, I have no idea how to command

I'll show you how my View is and my DAL.

View:

<div class="control-group">
    <label>Nome</label><asp:TextBox  ID="txbAlgNome" runat="server"></asp:TextBox><br />

</div>
<div>
        <asp:Button ID="button_cad_1"  runat="server" Text="Salvar" onclick="button1_cad_veiculo" />
</div>

View code:

using System;
using System.Collections.Generic;
using System.Linq; 
using System.Web;
using System.Data;
using System.Web.UI;
using System.Web.UI.WebControls;
using Geax1.Model;
using Geax1.DAL;

namespace Geax1.Views
{
  public partial class AluguelVeiculos : System.Web.UI.Page
  {
    protected void Page_Load(object sender, EventArgs e)
    {
        //enviando o nome para o SELECT no meu DAL
        _AluguelVeiculos aldata = new _AluguelVeiculos();

        aldata.Nomecliente1 = txbAlgNome.Text;

        _ListaNome.ListaNomeCliente(aldata);


        //preenchendo os campos do TextBox, após o select Like
        txbAlgNome.DataBinding = _ListaNome.retornaNomecliente();

      }
    }
  }

My DAL:

namespace Geax1.DAL
{
  public class _ListaNome
  {
    private static List<_AluguelVeiculos> lc = new List<_AluguelVeiculos>();

    public static void ListaNomeCliente(_AluguelVeiculos obj)
    {
        using (var conn = new MySqlConnection("server=127.0.0.1;Database=xpto;User ID=root;Password='';"))
        {

            MySqlDataAdapter adapter = new MySqlDataAdapter();
            adapter.SelectCommand = new MySqlCommand("SELECT nome, cpf FROM tab_cliente WHERE nome LIKE '%nome% ;", conn);

            DataSet dataset = new DataSet();
            adapter.Fill(dataset);

            foreach (DataRow linha in dataset.Tables[0].Rows)
            {
                _AluguelVeiculos cl_1 = new _AluguelVeiculos();

                cl_1.Nomecliente1 = Convert.ToString(linha["nome"]);
                cl_1.CpfCliente1 = Convert.ToString(linha["cpf"]);

                lc.Add(cl_1);
            }
        }
    }

    public static List<_AluguelVeiculos> retornaNomecliente() 
    {
        _AluguelVeiculos al = new _AluguelVeiculos();
        ListaNomeCliente(al);
        return lc;
     }
  }

}