What is the name of the Tajwid ruling when reading "e'tooni" instead of "i'tooni" in the third verse of Surat Al-Ahqaf?

To summarize the answer: When starting (a recitation), the hamzat al-wasl (connecting hamza) is pronounced clearly. If it is followed by another silent hamza, the second hamza is transformed into a long vowel letter (harf madd) of the same type as the preceding vowel's diacritic (a yā’ if the preceding vowel is a kasra, like in “i’tūnī” (ائتوني), and a wāw if it is a ḍamma, like in “u’tumin” (اؤتمن)). However, when continuing a recitation (without a pause), the hamzat al-wasl is dropped. It is recommended to learn the recitation orally from a shaykh.