Take Jigsaw as an example. When we decided to call our business Jigsaw, we knew that there was already a well-known clothing company using the name (as well as many jigsaw sellers), so we decided to set ourselves apart by creating an identity to go with the name.
Hence "complete the jigsaw".
As a marketing consultancy, Jigsaw's aim is to supplement a client's business by offering the expertise needed to complete their jigsaw. So, the name became more than a name, it became an identity and a mission statement.
A brand consists of many different things. Your logo and the associated strapline or mission statement, together with the graphic designs which are used on all of your company literature and promotional material. A brand is not simply a letterhead or a business card, it extends to your sales order forms, your fax headers, your website and your literature.
It is recognisably you.