The UN library is known by the name of

The correct answer is: C. Hammarskjoeld library.

The Dag Hammarskjöld Library is the official library of the United Nations. It is located in New York City, and is named after Dag Hammarskjöld, the second Secretary-General of the United Nations. The library was founded in 1946, and has a collection of over 3 million volumes. It is open to the public, and provides research services to UN staff, diplomats, and other researchers.

The other options are incorrect. Option A, “Nation’s library,” is not the name of the UN library. Option B, “U Thant library,” is the name of a library at the University of Rangoon in Myanmar. Option D, “Trygve Lie library,” is the name of a library at the University of Oslo in Norway.