The Jamia Hafsa Madrassa is linked to the Red Mosque, known for its links with Islamic militant terrorist.
A paper sign on one of the doors proclaims Bin Laden a “Shahid” (martyr). Bin Laden was killed in a raid by US commandos in 2011.
Pakistani troops raided the mosque in 2007. Dozens died later in clashes.
The BBC’s Shumaila Jaffrey in Islamabad says there are no chairs or any table in the library – just two computers on the floor.
The library is in a huge complex in the heart of Islamabad, part of which is still being built.
A spokesman for the madrassa said the new name was a tribute to Bin Laden, who was and Islamic “hero”.
The chief cleric there is Maulana Abdul Aziz. He warned that “if the government makes madrassas and mosques its target then Sharia (Islamic law) allows us to retaliate – if anyone will be harsh with us, they should not expect flowers in return”.
He also uses the library as his office. It has about 2,000 books – all of them related to Islam.
There are books about Sharia, Jihad and interpretations of the Koran in Arabic, Urdu and English, our correspondent reports.