When the University of Malaya campus was moved from Singapore to Kuala Lumpur in year 1958, a new hostel had been constructed and that hostel was called the Second Residential College, or Second RC.
After some time, the name of Second Residential College (Tuanku Bahiyah Residential College) was amended to Asrama Kedua, in accordance with the ambition of fostering nationalism at that time. Near year 1984, Asrama Kedua was changed to Menara Budi. 1993 witnessed the next change in the college name, now it is known as Kolej Kediaman Kedua.
On 24th July 2006, Kolej Kediaman Menara Budi was renamed to Kolej Kediaman Tuanku Bahiyah in honour of Her Majesty Tuanku Hajah Bahiyah Bt. Almarhum Tuanku Abdul Rahman, the 1st woman to become the Chancellor of University of Malaya.
Dr. Nahrizul Adib Kadri