//creat auto complete Collection
 AutoCompleteStringCollection collection = new AutoCompleteStringCollection();
//Connection String
 string connectionString="your connection string";
//creating connection String
SqlConnection con = new SqlConnection(connectionString);
//open the connection
con.Open();
//get the data from database
SqlDataAdapter ad = new SqlDataAdapter("select sname from tbl_Student", con);
DataTable dt = new DataTable();
ad.Fill(dt);
if(dt.Rows.Count>0)
{
for (int i = 0; i < dt.Rows.Count; i++)
{
  //add the student name into auto complete collection
  collection.Add(dt.Rows[i].ItemArray[0].ToString());
}
}
//after adding the student names into auto complete collection bind the collection to textbox
textBox1.AutoCompleteMode = AutoCompleteMode.Suggest;
textBox1.AutoCompleteSource = AutoCompleteSource.CustomSource;
textBox1.AutoCompleteCustomSource = collection;