Clicker Training for Dogs
Few clickers have exactly the same sound and your dog most likely has perfect pitch. If you take two clickers and listen while you click one and then the other, even you will notice the difference in its pitch and volume.
In a class situation where a dozen dogs are being clicked, your dog will be able to discern his clicker from all the others in the first few clicks. If the next week you take a different clicker to class, he will recognize it as easily as did the week before.
That doesn't mean you can't use one clicker for all of your dogs or that you shouldn't use just any clicker you can lay your hands on regardless of which one you used last for an individual dog. In fact, I recommend having and using several clickers. Consider changing clickers as one of the various criteria your dog will encounter in his training life, and allow him to work through it.
Having different clickers for different dogs is not a bad thing, but be aware that if you can't find Dog #1's clicker and you use it to train Dog #2, Dog #1 will become upset. He'll get over it, of course, but only after some stress. He wants to play the training game himself, which is upsetting enough. Using his clicker while training the other dog is stressful.
So, keep clickers everywhere and use them with any dog at any time to eliminate unnecessary stress over whose clicker is being clicked.