It may be or include a business name or tagline. It may or may not be incorporated into a logo. In fact it can be anything which can be represented graphically which, perhaps surprisingly, can even include:
all of which can be part of your brand.
Your name or logo can be registered as a Trade Mark provided it is sufficiently distinctive and clearly marks out your product from others.
Even if your brand is not registered, it may still be protected by the law of passing off which prevents anyone using a confusingly similar brand. On the whole, registered rights are easier to enforce.