It is hard to imagine anyone living in our consumer society who is not effected by branding and brand loyalty. Companies with products may have their own brand then individual brands for their products. A good example of this is chewing gum. The manufacturer may have their own logo, their brand but the actual range of gum they produce may have a brand for each product.
For service industries and professions a particular package of services can have a brand, we see this often with phone and media companies. So the 'sub' branding can be changed but the company branding, part of its 'corporate identity' can stay the same. A brand isn't necessarily a logotype although logos and graphic devices are often used if for no other reason than to simplify marketing. A distinctive logo is a great way to identify a brand. Most in business would agree it's a good idea to have a company logo.
There have been many in-depth studies, this is a very broad topic so a simple question like "How does branding work?" isn't easy to answer with a few words but we will try by example.
In our kitchen we have tea and coffee. We choose these products based on their flavour, availability and cost. Invariably, if the cost is the same or within a few pence and there may be no 'real' preference on taste and a range of products are available we will buy one particular brand because, we bought it before and it was fine. Our purchase decision is based on a variety of factors including trust. Having used a product already, we trust it will be good again.
A long standing and trusted soap manufacturer changed their formula in the 2000's from one that had been in use since the 1920's. Customers continued buying the soap even though many complained it was "not as good" and even formed pressure groups to convince the company they should return to their original formula.
One could argue that Apple computers who have had periods of severe difficulties have survived because of brand loyalty. This list goes on and on where a companies reputation is encapsulated with its brand. When customers and clients feel they can trust the brand it becomes extremely powerful and important to the success of a business.
One could argue that with health care brand loyalty is irrelevant because if course if one is healing then once that person feels better, the job is done and one would not wish them to return. This ignores the trust element, a person who trusts your 'brand' even if they no longer need your services is in fact an asset for your business.
Having helped a customer one would hope they will inform their circle and help promote your service further afield. For this reason, referral consultations are vital for long term business development for services especially when the subject has a sensitive nature. Personal recommendations are like gold to sales teams so one should value every opportunity. Where your branding can help in these scenarios is simple, it makes it easier for those recommending your services to pass your details on, especially when your service information can be found on-line.
Your website can become a resource for those customers you have helped. One can have sections of content specifically tailored for existing customers and of course those you have previously helped where they can 'log in' to view exclusive content. On-site forums are available too so one could have on-going correspondence with your client-base forming new groups and helping promote your business and your therapy.