At one time, AT&T and T-Mobile wanted to merge but were prevented from doing so by the Justice Department. The government maintained that to permit the merger would eliminate choices for the consumers because these companies represented the majority of the cell phone service industry. What is the name given to this kind of merger?

If such a merger happened between the two largest companies in the market, it will turn in to a "Monopoly".

Explanation:

A Monopoly is a condition where a single entity in the industry possess the exclusive control of the supply or trade in that industry. Monopoly is not considered to be beneficial to the customers as the Monopolistic organization holds a powerful grip of the market, specially when it comes to the quality of the product and the price. Customers have only a little to say about the quality or the price as they are primarily decided by the monopoly.

AT&T AND T-mobile both hold a significant market share in the telecommunications industry.

A merger of these top two companies would mean that they will have the ultimate authority and power to decide on the data costs, call chargers and etc. This will probably eliminate the consumers' choice to chose better or suitable options as the rest of the other organizations operating in the industry are not as capable as these companies to cater quality services to the customers.

Apart from this, monopoly could arise in several ways such as,

Having exclusive rights to access natural resource Patent rights Logistical advantages (if the extraction and the delivery of certain resources are too expensive, this may naturally lead to monopoly condition) Government interventions and regulations