The correct option is C it was named after Sangama, the father of Harihara and Bukka
Vijayanagar empire was established in 1336 by Harihara I and his brother Bukka Raya I of Sangama Dynasty. It was ruled successively by five dynasties namely- Sangama dynasty, Saluva dynasty, Tuluva and Aravidu dynasty. The first dynasty of the empire of Vijaynagar is known as Sangama because it was named after Sangama, the father of Harihara and Bukka.