How do I organize my Actions in Swing?

I am currently replacing my anonymous ActionListeners

new ActionListener() {
    @Override
    public void actionPerformed(final ActionEvent event) {
        // ...
    }
}

with class files representing actions:

public class xxxxxxxAction extends AbstractAction {
}

However, my GUI is able to perform a lot of actions (eg. CreatePersonAction, RenamePersonAction, DeletePersonAction, SwapPeopleAction, etc.).

Is there a good way to organize these classes into some coherent structure?

You can keep your actions in a separate package to isolate them. Sometimes, it is useful to keep them in one class, especially if actions are related or have a common parent, for example:

public class SomeActions {
    static class SomeActionX extends AbstractAction {
        @Override
        public void actionPerformed(ActionEvent e) {
        }
    }

    static class SomeActionY extends AbstractAction {
        @Override
        public void actionPerformed(ActionEvent e) {
        }
    }

    static class SomeActionZ extends AbstractAction {
        @Override
        public void actionPerformed(ActionEvent e) {
        }
    }
}

Then to access them:

JButton button = new JButton();
button.setAction(new SomeActions.SomeActionX());