4U-Corp was created when the Hereti-Corp of the Dimension of Rain combined with several other companies. This was a direct result of the R&D Wars. Before the wars started Hereti-Corp was already very powerful, and had close ties to the military after selling them Riff's stolen REA-1 (aka Mark-19) designs. After the wars Hereti-Corp, which had access to more advanced materials and weapons due to its military contracts and probably fared better, absorbed the weakened factions. Dr. Schlock publicly led Hereti-Corp and later 4U-Corp, and built 4U City. After it was finished, and apparently for no reason, the newly christened His Masterness used a giant weaponized DFA to flux every other being out of the dimension. (except for those inside 4U City) It is unknown what became of 4U-Corp after the City was constructed, it most likely made a transition into becoming a full-time dictatorship government and is still running things. They also seem to have control over the dimension's version of Oasis (named Harbinger).
4U-Corp's name and logo comes from the four words that begin with the letter "U" that describes their company and City. They are: Universal Unified Ubiquitous Utopia.
The name is probable also a reference to how the city was made to accomidate the population, that is, it was built "for you. " (speculation)