What is the name of an enclosure designed for surface mounting with swinging doors or covers?

The correct answer is a cutout box, as it specifically refers to an enclosure designed for surface mounting that features swinging doors or covers. Cutout boxes are typically used in electrical installations to house components and to provide access for maintenance and management of electrical circuits and devices. Their design accommodates the need for easy access while ensuring the necessary protection for electrical components, making them suitable for installation in various settings.

In the context of other options, a distribution box usually serves a different purpose, typically related to distributing power across multiple circuits but does not specifically focus on the design of swinging doors or covers for surface mounting. A service panel is an essential part of an electrical system but is primarily for circuit protection and does not share the same specific design characteristic as a cutout box. A wall box is generally used within walls for containing electrical devices but does not imply the same surface-mounted, swinging door feature as cutout boxes.