Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Appearance of Imam Al-Mahdi is one of the signs of the Last Hour which is not mentioned in the Qur'an, but it is mentioned in the sound Sunnah. Many details such as his name; description, the place where he will appear etc. are mentioned in Sunnah. The Prophet (Sallallahu Alaihi wa Sallam) said: "This world will not come to an end unless a man from my family rules over Arabs, his name will be like my name and his father's name will be like my father's name."
No doubt that Sunnah is as authentic as the Qur'an, so believing in it is as believing in Qur'an. Allah says: "And whatsoever the Messenger (Muhammad SAW) gives you, take it, and whatsoever he forbids you, abstain (from it), and fear Allâh. (Al-Hashr 59:7)
Allah knows best.