The simplest version of the name of the Department sounds like officers working in it. For example, if the division leaders, Director of marketing, advertising, public relations, the division may be called "the Directorate of marketing and advertising."
If the Department managers of different disciplines but linked by a common project or dealing with customers, it is possible to designate the Department of the common name describing the ultimate goal of the activities of these employees. For example, if the division consists of designer, Manager, negotiations with the client (account Manager, copywriter and Manager in charge of creative, the division can be called "Product Department", ie there is developed a certain product or service for the customer.
The Department in which managers collect claims from customers, their complaints, warranty cards, can be described as "quality Department" or "Service Department".
Managers, whose function is to answer incoming calls and inform potential customers about the company's services, promotions, etc. are usually located in the Department "Call center". But, if it's a name you don't like the division you can rename to "Information". The name of the Department sounds more noble and not associated with a steady stream of phone calls.
Call the Department and jointly with the employees of the company. So, will announce the contest about the name of the Department, place the box on the ground floor in the office where it will be possible to put the workers in their proposals. After 10 days, give each of the proposed name of the division and vote for the best offer.
Importantly, the name of the Department should correctly display its activity. Therefore, if the Department has more than one dozen people, and each employee has their own spec work, it should be this Department is divided into two, and the names give them more specific. For example, instead of one of the Department "advertising Department", it is possible to organize the "Department of outdoor advertising" and "Department of Internet advertising."