How to refer/identify to buttons generated/iterated from nested for-loop?

Question

I am trying to figure out how to refer to buttons generated from a nested for-loop. I am trying to assign a value to each button which can interact with a switch in an action listener. Would the buttons already have referencable names/IDs in my code, given as follows? Should I instead assign variables to each button? How might I do that? I am a beginner, btw.

        for (int row = 0; row < rows; row++)
        {
            for (int column = 0; column < columns; column++)
            {
                 JButton button = new JButton();
                 buttonPanel.add(button);
                 button.addActionListener(new coolActionListener());
            }
        }