Final answer:
In Kincaid's 'A Small Place,' the building named after the Prime Minister is the library.
Step-by-step explanation:
In Kincaid's A Small Place, the building that is named after the Prime Minister is the library. The book is a critique of post-colonialism in Antigua, and Kincaid uses the library as a symbol of the island's neglect and the legacy of colonialism. The library had been located in a building called the Carnegie building but had been moved and renamed after the Prime Minister Vere Cornwall Bird. The library's state of disrepair and the irony of naming it after a leader is not lost on Kincaid, who points this out poignantly in her work.