Yes, dog training can be and should be fun for your Schnoodle.
My husband and I stumbled upon teaching Toby the names of his toys. I say "stumbled" because we did not do this intentionally at first. We just started to notice Toby would go for a toy by its name after saying it consistently a few dozen times.
Dogs are very intelligent, trainable animals and any learning opportunities should not be wasted. Don't treat teaching your dog its toy's names as a strict, command-type lesson. Just do it gradually. In no time, your Schnoodle will be searching for every toy he/she owns by name (and then you will have to buy more dog toys).
Dog Training Aids at PetSmart.com