You should replace the hard coded parameters with sql parameters, but here is a general idea of what you'll need to do here. Using your present sql query.
MySqlConnection sqlConn = new MySqlConnection();
MySqlCommand sqlCmd = new MySqlCommand();
string sSql = "SELECT id FROM caregiverdatabse WHERE name Like '%" + caregiverNameDisp.Text + "%'";
sqlConn.ConnectionString = "Server=" + server + ";" + "Port=" + port + ";" + "Database=" + database + ";" + "Uid=" + uid + ";" + "Password=" + password + ";";
sqlCmd.CommandText = sSql;
sqlCmd.CommandType = CommandType.Text;
sqlConn.Open();
sqlCmd.Connection = sqlConn;
MySqlDataReader reader = sqlCmd.ExecuteReader();
List<string> results = new List<string>();
while (reader.Read())
{
results.Add((reader["id"].ToString());
}
reader.Close();
sqlConn.Close();
Keep in mind you can add the reader results to a string, to a list like above, whatever you want to do with it.