clear your dataset every time before it loads new data from database. and also your combobox.
public void Bank_Name()
{
cmbCust.items.clear();
DataSet ds = new DataSet();
Ds.Clear();
SqlConnection cone = new SqlConnection(cnstd);
cone.Open();
SqlDataAdapter adpi = new SqlDataAdapter("Select distinct Cust_Name from Customer", cone);
adpi.Fill(ds);
cmbCust_Name.DataSource = ds.Tables[0];
cmbCust_Name.DisplayMember = "Cust_Name";
cone.Close();
}