What term describes using a word to represent something closely related, like saying "Washington" to refer to the government?

The term that describes using a word to represent something closely related, such as employing "Washington" to refer to the government, is metonymy. In this rhetorical device, a word or phrase is substituted for another with which it is closely associated. This allows for a more vivid or concise way to convey meaning by drawing on the connection between the two concepts.

Metonymy is often used in literature and speech to evoke a deeper understanding or to create a specific image in the mind of the audience. For instance, in saying "The White House announced a new policy," "The White House" symbolizes not the building itself, but the president and his administration.

In contrast, synecdoche involves a part representing the whole or vice versa, which is a distinct concept from metonymy. Apostrophe refers to addressing an absent person or an abstract idea, while colloquy describes a conversation or dialogue, which does not fit the definition provided in the question regarding representation through association.