What are the names of the twenty-five reciters, and I am not concerned with the history?

The twenty-five reciters are not known. However, there are the ten Mutawatir reciters whose recitations are well-known, and there are four other reciters whose recitations are irregular (shādhdhah) and not permissible to recite with. These are: Al-Hasan al-Basri, Muhammad ibn Abd al-Rahman known as Ibn Muhaysin, Yahya ibn al-Mubarak al-Yazidi, and Sulayman ibn Mihran al-A'mash. These four, along with the initial ten, are known as the fourteen reciters. And there are the seven reciters, who are the first seven of the ten.