When you run the following you will see the duplicated JLable text. It's not readible because of that.

When you comment out paint method, it looks fine.

import java.awt.swing.*;
import java.awt.swing.tree.*;
import java.awt.*;

class MyTreeCellRenderer extends JPanel implements TreeCellRenderer
{
    JLabel alabel = new JLabel("a label");

    public MyTreeCellRenderer(){
        super(false);
        setLayout(new FlowLayout());
        setBackground(Color.white);

        add(alabel);
    }
    
    public void paint(Graphics g){
        super.paint(g);
       alabel.paint(g);
    }

    public Component getTreeCellRendererComponent(JTree tree,
                                                  Object value,
                                                  boolean selected,
                                                  boolean expanded,
                                                  boolean leaf,
                                                  int row,
                                                  boolean hasFocus){

        DefaultMutableTreeNode node = (DefaultMutableTreeNode)value;
        alabel.setText((String)(node.getUserObject()));

        return this;
    }
}

public class PaintTest extends JFrame
{
    JTree tree = null;
    MyTreeCellRenderer renderer = null;

    public PaintTest(){
        DefaultMutableTreeNode top = new DefaultMutableTreeNode("TOP");
        DefaultMutableTreeNode catagory;
        DefaultMutableTreeNode composer;
        DefaultMutableTreeNode style;

        // Classical
        catagory = new DefaultMutableTreeNode("Classical");
        top.add(catagory);

// Beethoven
catagory.add(composer = new DefaultMutableTreeNode("Beethoven"));
composer.add(style = new DefaultMutableTreeNode("Concertos"));
style.add(new DefaultMutableTreeNode("No. 1 - C Major"));
style.add(new DefaultMutableTreeNode("No. 2 - B-Flat Major"));

composer.add(style = new DefaultMutableTreeNode("Quartets"));
style.add(new DefaultMutableTreeNode("Six String Quartets"));
style.add(new DefaultMutableTreeNode("Three String Quartets"));
style.add(new DefaultMutableTreeNode("Grosse Fugue for String Quartets"));

// Mozart
catagory.add(composer = new DefaultMutableTreeNode("Mozart"));
composer.add(style = new DefaultMutableTreeNode("Concertos"));
style.add(new DefaultMutableTreeNode("Piano Concerto No. 12"));
style.add(new DefaultMutableTreeNode("Piano Concerto No. 17"));


        renderer = new MyTreeCellRenderer();
        tree = new JTree(top);
        tree.setCellRenderer(renderer);

        getContentPane().add(tree);
        setSize(300,300);
        show();
    }


    public static void main(String[] args){
        new PaintTest();
    }
}