The Imamah is the legitimate succession of the Prophet Muhammad (SAWA). No prophet left his Ummah with out informing them clearly about his legitimate successors who should lead people on the right path and prevent deviation. Quran has mentioned the Imamah in many verses e.g.

(And We made them Imams who call people by Our Order) (Sura 21, verse 73).

(And We made from them Imams who call by Our order) ( Sura 32, verse 24).

Allah (SWT) ordered all Muslims to obey Allah, the messenger and the divine leaders ( the Infallible Imams) (Sura 4, verse 59).

Many books were compiled by prominent scholars in Quranic verses related to Ahlul Bayt (AS) e.g. 

Sunni Muslims have no evidence in Quran or authentic Hadeeths to justify the leaders whom they follow from Saqeefa, Bani Umayyad, Bani Abbas and till now.

The names of the Infallible Imams are not mentioned in Quran for a great wisdom known by Allah (SWT) as Allah (SWT) did not openly mentioned many other important matters like the number of Rak'ats of Obligatory Salah. He knows the reason behind that. He ordered in Quran all Muslims to obey the Prophet (SAWA) and the Prophet informed the Muslims about the number of Rak'ats of every obligatory Salah, and informed the names of the Infallible Imams as well.

Imam Jafar Al-Sadiq (AS) was asked: Why the names of the Infallible Imams were not mentioned in Quran? He reportedly replied: Ask those who put this question: Where did Allah mention in Quran the numbers of Rak'ats of Salah?

The Prophet (SAWA) only informed about the numbers of Rak'ats and the names of Infallible Imams.

Wassalam.