Why not? If you have a unique hairstyle and want to commercialize it, you can actually brand it with the patent and trademark. A hairstyle is a human creation and like most creations it can be an asset, and in this case it is an intellectual property. If it becomes a trademark, others must get your permission to copy it. However, you will be required to officially bring it with the Patent and Trademark Agency first and pay the official fees and make the necessary paperwork for filing. Of course, a brand needs a name, so you have to come up with one, as unique as possible, so that the brand will not have reasons to reject it. But for all purposes, the brand is a way of preventing others from using the same idea and forming neither for their own or commercial purposes.
However, whether or not you will be allowed to brand it will depend on the brand office, but there is a very good chance that it will be allowed. To be allowed for a brand, its shape must be unique, something that can stand out from the crowd, so that people can identify it as different from the norms. Like company logos, your particular haircut must be reproducible and it must also be identifiable by a name. For the purposes of commerce, form and name should be easily identified so that others will be able to communicate with others about it.
A hairstyle need not only consist of hair alone, because it is also possible to weave it with some other objects such as hair bands and bracelets. In fact, you can make it unique with a large selection of hair accessories or with something you design yourself. And remember, if it's new and nobody has it, you can download it and do it yourself. Then you can commercialize it and license other salons to recreate the particular hairstyle. Of course, you must make it so desirable that others would like to copy it and pay you a fee to do so.
And keep in mind, maybe the people who had promoted fashion shows should have applied for trademarks for all lasses who had been sporting unique hairstyles as part of fashion shows!
But what if someone copies it without paying you for the idea? Well, getting a brand is one thing, enforcing it is another thing altogether! It is important that you have to report any form of infringement and to take legal action yourself! But even if you don't get a cent for the thought and assume that the specific hairstyle will be a hit, only people who talk about it will inevitably increase the value of your idea and brand. If it's a buzz, you'll take advantage of it many times over. In addition, the brand does not need to be associated with just one hairstyle, as you can also use it for other things, provided you obviously also register it under other product categories with the branding. The possibility is unlimited because we not only talk about people, but also others like pets and everything that needs a unique dressing!