You could require a booking approval process, where the user selects their time slot, then waits for booking confirmation from Hairstylist A. Before confirming, Hairstylist A could use their own judgement in deciding if the request is phony or not.
If a simple user registration is not out of the question for this scenario, you could require login to where you could limit the number of appointments any one user can book. Identify the user via email address and/or phone number and/or some other unique means, and then keep track of if that unique user has reached their limit.
One thing I have seen medical practices do is to charge a fee if the customer does not show up. This works best if billing information is already disclosed. People take these kinds of appoints a bit more seriously when money is on the line. Whether or not this would be a hinderance to your clients is something to consider.
With any process there are pros, cons and potential ways for abuse. Generally these types of decisions are not about how to completely eliminate abuse, but more about how to reduce the likelihood of it occurring. Any solution you put in place someone likely will find a way around it at some point. You just have to ask yourself how much effort you want to put into prevention.
One important thing to ballance is to not make it too inconvenient for honest customers to use your system, due to complicating the process with steps taken to curb the potential cases of abuse. (For some reason DRM comes to mind when thinking about this concept)