What is the name of the special prayer performed on Eid al-Fitr morning?

The special prayer performed on Eid al-Fitr morning is Salat al-Eid.

Salat al-Eid is a communal Islamic prayer held after sunrise and before noon on the first day of Shawwal. It consists of two rak'ahs and is normally followed by a khutbah, or sermon. Unlike the Friday prayer, the sermon traditionally comes after the prayer.

The prayer has distinctive extra takbirs—declarations of “God is greatest”—whose number and placement vary among Islamic legal schools. It is commonly held in a mosque, large prayer hall, open field, or special Eidgah. No adhan or iqama is called immediately before it.

Salat al-Eid is not the same as Tahajjud, a voluntary night prayer; Taraweeh, the Ramadan night prayer; or Jumu'ah, the weekly Friday congregational prayer. Its legal status also differs by school: some regard it as obligatory or necessary, while others classify it as a strongly emphasized Sunnah.