There is no such thing as Palacio de Oriente in Madrid
The name of the palace is "Palacio Real" and "Palacio de Oriente" is incorrect although not totally uncommon.
The name of the palace, Palacio Real is rather obvious. The name of the square to the east of the palace is "Plaza de Oriente", also for obvious reason as it is to the Orient of the palace.
Because of the similarity of the words "plaza" and "palacio" and some mental laziness, some people say "Palacio de Oriente" which makes no sense because the palace is, in fact, WEST of the square and west of Madrid.