The Korean Dream is about the realization of a united nation, going all the way back to the aspirations of the independence movement.
There is a reason why both the Republic of Korea and the Democratic People’s Republic of Korea used the ROK (Republic of Korea), as not only the name of the South Korea country, but also in the name of the North Korean country.
It’s because the aspiration of the independence movement was to create a republic of Korea. The reason why they chose acronyms is because they wanted to have claim to the creation of that Republic of Korea.
The aspiration of the independence movement was to create a Democratic Republic.
The unification of Korea as outlined in the Korean Dream is to create a nation that reflects the noble aspiration that inspired the independence movement.