In the traditional sense, not really, and applying different definitions and standards that don’t fit the nature of the industry in an attempt to do so doesn’t get the job done. There are many differences between dentists and their practices of course. Some dentists have busy practices with large staff while others are recognized for doing fantastic work within their smaller practices. Some have better-equipped practices and offer more services, while some offer specialty services. Clearly, the nature and overall quality of dental practices can differ greatly, but practically speaking these differences don’t brand the dentist, nor represent different brands of dentistry.
There are several actual brands of dentistry that exist today, some of them quite notable. ClearChoice® is one that comes to mind, along with various brands of products used for dental treatment- Invisalign, All--on-4, and Snap-on Smile, for example. There are also several different types of dentists who specialize in different types of dentistry- types, not brands of dentistry.
When it comes to personal and professional attributes, some dentists are certainly nicer, more gentle, sensitive, kinder, smarter, more knowledgeable, and more personable than others. While these styles, traits, and attributes may accurately describe certain practitioners (and be preferable and more desirable to the consumer), they don't really represent a brand of dentist or dentistry. The consumer’s thoughts, feelings, attitudes, and how they speak of a particular dentist is more likely than not what determines that dentist’s brand.