In the history of Bani Ummayid rule in the beginning of Islam, two Yazids have been named. The first was Yazid Ibn Abi Sufyan and the second, was Yazid Ibn Muawiyah. As you can see, the name of the son of Abu Sufyan, who is also the brother of Muawiya, was Yazid. Muawiyah named his own son after his brother Yazid. This Yazid later ordered the killing and martyrdom of Imam Hussein (A) during the tragedy of Karbala. Ibn Abdil Birr in his fifth century book, Isti’ab, has mentioned Yazid ibn Abi Sufyan.
 Ibn Abdil-Birr, Al-Isti’ab, vol. 4, pg. 1575.