How authentic is the story narrated that Adam, peace be upon him, named one of his sons Abd al-Harith (Slave of al-Harith) upon the advice of Iblis, after the death of three of Eve's children, and is this story found in Islamic education textbooks in Saudi Arabia, and is there any Hadith in Al-Tirmidhi concerning it?

The story you asked about was narrated by Al-Tirmidhi, Al-Tabarani, and Al-Hakim, on the authority of Samurah, from the Prophet (peace be upon him). Its essence is that Iblis asked Eve to name her son "Abd Al-Harith" (servant of Al-Harith) so that he would live, and she did so. Sheikh Al-Albani graded this story as weak.