The solution was to use a ContainerListener to detect a component added through the implemented componentAdded method. When a component was added to the JTabbedPane, I called a method to update the tab names with the components name, set via .setName().
public void componentAdded(ContainerEvent added) {
updateTabs();
}
public void updateTabs() {
for (int i = 0; i < tabbedPane.getComponents().length; i++) {
tabbedPane.setTitleAt(i,
tabbedPane.getComponents()[i].getName());
}
}