Final answer:
The Ismailis are called after Imam Ismail, the seventh Imam in the Ismaili branch of Shia Islam, not to be confused with Shah Ismail of the Safavid dynasty.
Step-by-step explanation:
The Ismailis are called after Imam Ismail, who was the son of Imam Jafar al-Sadiq and the designated successor according to the Ismaili branch of Shia Islam. However, it is crucial to distinguish between the historical figure of Imam Ismail and Shah Ismail, who was the founder of the Safavid dynasty and claimed to be the Mahdi, the messianic figure in Islam. The Shia branch of Islam considers the leadership of the Muslim community, or ummah, to be a right inherited through the Prophet Muhammad's family, specifically through his cousin and son-in-law, Imam Ali, and Ali's wife Fatima. The lineage of Imam Ali is important as it represents the direct line of succession for Imams in Shia Islam. While the majority of Shia Muslims, known as Twelvers, believe that the twelfth imam went into hiding and will return to establish justice, the Ismailis hold a different perspective on the succession after Imam Jafar al-Sadiq, believing Imam Ismail to be the rightful successor.