This name has come only once in a verse of the Qura’n. There is the great oath in the second verse of Surah Buruj that says, “And by the promised Day.” The day that has been promised to all and the day all the apostles had promised about.
Some commentators have declared the leaving of the graves as the Promised Day or the day that is regarded as the day of intercession by the Messenger but these meanings are included in the first meaning.
A point to note is that this day has been mentioned after the oath by the heavens which has many constellation and the importance of that day is equal to the importance of the heavens. If the Day had not been there then the creation and existence of the heavens and this elaborate system would have been useless and it would not have merited the creation of this great system.
A similar name can be found in verse 83 of Surah Zukhruf that says, “So leave them to speak nonsense and play until they meet the Day of theirs which they have been promised.”