Why didn't we keep the name East Pakistan since we led the movement and created Pakistan? I am curious.
Even after partition this Province retained the name East Bengal for many years. Later, when I do not remember, the name was changed to east Pakistan. Before Pakistan Movement started in the sub-continent, Chodhury Rahmat Ali foresee two separate entities in the east and west. He named the east as Bangistan.
This Province was called Subeh Bangalah by the Delhi Mughals. Before that it was called Gaur. However, historians believe it was named as GHOR and was given by the Turkic Bakhtier Khilji. But, the local Hindus could not pronounce it properly, so the name changed to Gaur.
This Gaur was called Lakkhanabati before the muslim occupation. However, for the immigrant Muslims it was very difficult to pronounce. So, the name changed to Lukhnouti by the immigrant muslims.
This name has a historical background since the Mughal time. So, it was accepted by the people who inhabit it. By the way, I do not think if there were two separate muslim countries fornmed in 1947, the name would have been east Pakistan. Rather, it would have either been East Bengal or Bangladesh.
Pakistan Movement was a symbolic movement the purpose of which was to build one or two states in the muslim majority parts, as declared in the Lahore Resolution. This Resolution did not specify the name of the would be country. Before 1971 all the Bangali nationalist parties would say of Lahore Resolution to get Provincial autonomy or outright separation.