In what language, since you posted this in Processing Implementations?

If that's by error and you are talking about Java, you can use instanceof or getClass.
But it is better to make all your classes to implement a given interface describing their common behavior (eg. all of them have an update() and a draw() method), and to rely on this behavior (customized per class) rather than using instanceof, cast and other unreliable (because relying on runtime instead of compilation) discovery methods.

If you want the class name of obect foo you can print it using

1. println( foo.getClass().getName());

Thank you both for your replies.
As with many things it is so obvious afterwards,
I feel slightly embarrassed at having had to ask!

No problem here, it isn't something in the reference of Processing, and not obvious in the Java reference anyway.
I just wanted to point out than in regular Java programming, we rarely use getClass() (mostly for serialization and such), and usages of instanceof should be kept to a minimum, because there are better ways to do that!
Since it seems to be for Java, I just move the topic to Programming Questions.