With regards to the reason why the reason why yawm ul qiyaamah (the Day of Standing) is so called,  Shaykh Muhammad ibn Saalih al ‘Uthaymeen rahimahullaah states:

And it is called yawm ul qiyaamah for three reasons:

1) The qiyaam (standing) of the people from their graves, as per His statement, He the Most High:

The Day when the people will stand before the Lord of all the Creation.
Soorah al Mutaffifeen (83)

2) The qiyaam (standing) of the witnesses, as per His statement, He the Most High:

We will indeed make Our Messengers victorious and those who truly believed in the life of this world; and the Day when the witnesses will stand forth.
Soorah Ghaafir (40) aayah 51

3) The qiyaam (establishment) of justice, as per His statement, He the Most High:
 
And We shall set up Balances of Justice on the Day of qiyaamah.
Soorah al Anbiyaa (21) aayah 47

(Al qawl ul mufeed (2/118) of Shaykh Muhammad ibn Saalih al ‘Uthaymeen rahimahullaah, translated by Nasser ibn Najam)