The most accurate response for why the Ottomans chose the term "sultan" for their leader is:
The name gave the impression Ottoman rulers were liked by caliphs.
The term "sultan" implies authority and power, and its use by the Ottomans helped establish their legitimacy and status in the Islamic world, particularly in relation to the caliphate, which was a significant source of religious and political authority. The use of the title allowed the Ottoman leaders to position themselves as significant political figures, historically connected to the Islamic leadership.