If you have a small dog that you think might make a good riding companion, the first thing you will want to do is to work with them to make sure they are not frightened by the loud noises your motorcycle may make. For smaller dogs, you will be able to purchase a leather mesh doggie crate that will ride over the passenger section of the bike like a saddlebag. By taking the dog out on trips, you can better determine the attitude of your passenger and know whether or not this is going to be something that you can do on a regular basis or for a long ride. Not all dogs are going to love biking, but some will.
In fact, some small dogs even ride well enough to sit on the back of the bike with very minimal restraints, but this is not something you should attempt until you are certain of your dog's riding capabilities. You do not want to risk putting a dog on the back of the motorcycle with nothing more than a small harness if they do not have the fortitude to stay on the seat. If they struggle against the harness or try to get off of the bike, then there could be a big problem.
However, there are a number of different riding options, and one of them is sure to fit your specific pooch and their riding habits. If you are concerned about them getting wind in their eyes or other worrisome flying objects, then there are even specifically designed goggles that will fit over your dog's head. There are also leather doggie jackets and other outerwear that can be easily personalized with neat and interesting motorcycle patches. Before long your dog will have their own riding style.