It is permissible to name a child Yazid (یزید). There have been Sahabah, Tabi'een, muhadditheen, and jurists who bore this name. Some of the Sahabah, may Allah be pleased with them all, who were named Yazid are listed below:
Yazid ibn al-Harith (may Allah be pleased with him)
Yazid ibn Qatadah (may Allah be pleased with him)
Yazid ibn Abi Sufyan (may Allah be pleased with him)
Allah the Almighty knows best.
Darul Ifta Al-Ikhlas, Karachi.
الاستیعاب فی معرفة الاصحاب: (1573/4، ط: دار الجیل)