Mark,
This depends on the JCSplashScreen class... is this your class, do you have the source, can you extend it? If any of these are the case, either modify or extend the class to allow you to set a
String and also modify the paintComponent() method to draw a string over the image using the drawString() method of Graphics.
Even if you don't have the code to the class, and can't override it, you can make a BufferedImage of your image and draw the string on that, then send the buffered image to the splash screen class.
If you need any help on either of these approaches, just post your questions!