How can I create a connection manager and process query result in multiple ways? (Java)

sorry for the long post. I will try to be as clear as possible.

I'm creating an app for my Software Engineering class and I am in front of this problem:

As suggested by one of our teachers, I should assign the responsibility of managing database resources to DAOs. I created an abstract DAO class which creates the connection to my database (it's a PostgreSQL database) to manage every connection in a single class, which opens the stream and closes it after the result of a query is consumed through an abstract method that will be implemented by many concrete DAO singleton classes. At the end of the post, there is an example of what I coded.

Everything seems fine to me because thanks to the inheritance I can connect several and different DAOs to the database, that is my case. The true point now is that I can't figure out how can I process the data inside the ResultSet, without taking care of the query that was made or what method of one of the concrete classes asked for connection.

P.S.: I tried to look for some patterns/solutions but I didn't find anything that fit my case. P.P.S.: I know that I should use DataSource instead of DriverManager, but this is what was taught in class.

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The abstract class Example:

public abstract class AbstractDAO {
  private static final String URL = "my_url";
  private static final String USR = "my_usr";
  private static final String PWD = "my_pwd";

  private final Logger logger = Logger.getLogger(getClass().getName());

  protected void connect(String query){
      try(Connection con = DriverManager.getConnection(URL, USR, PWD);
          PreparedStatement pst = con.prepareStatement(query)){
          ResultSet rs = pst.executeQuery();
          processResult(rs);
      }catch (SQLException e){
          logger.log(Level.SEVERE, e.getMessage());
      }
  }
  // abstract method to process atomically the result in each DAO.
  protected abstract void processResult(ResultSet rs) throws SQLException;
}

The concrete class Example:

public class ConcreteDAO extends AbstractDAO {
  private static ConcreteDAO instance = null;

  private ConcreteDAO() {
      super();
  }

  private static synchronized ConcreteDAO getInstance() {
      if (ConcreteDAO.instance == null) {
          ConcreteDAO.instance = new ConcreteDAO();
      }
      return ConcreteDAO.instance;
  }
  @Override
  protected void processResult(ResultSet rs) throws SQLException {
      int numCols = rs.getMetaData().getColumnCount();
      while (rs.next()) {
          for (int i = 1; i <= numCols; i++) {
              System.out.println("\t" + rs.getString(i));
          }
          System.out.println("");
      }
  }
  public static void main(String[] args) {
    String query = "select name, surname from test";
    getInstance().connect(query);
  }
}