What is Dr. José Rizal real name?

Dr. José Rizal was a Filipino nationalist, writer and polymath active at the end of the Spanish colonial period of the Philippines. He is considered the national hero of the Philippines. His complete name was Dr. José Rizal Protasio Mercado y Alonso Realonda. Many wonder why he used “Rizal” while his father was Francisco Mercado. He should have been Jose Mercado, right? So, why did Rizal’s surname become Rizal instead of Mercado?

Some of the explanations with this are:

Jose’s real last name, Mercado, during those times was a hot name, targeted by the Spaniards. He changed his surname to protect his identity. So he just used his middle name, Rizal, instead, which was considered as illustrado during the Spanish time and entails the benefits a Spaniard can get. Second, there was Spanish law to change the last name of Filipinos those times.Mercado sounded a common name and there were lots of people having that surname already who were not really relatives of Rizal.