Oracle Corporation

The Oracle of Delphi used to provide answers to questions [...] I have no idea why someone would use that name in regards to a database.

In 594 BC, Solon, the Athenian lawgiver, seeking to capture the island of Salamis from Megara and Cirrha was told by the oracle:

First sacrifice to the warriors who once had their home in this island,
Whom now the rolling plain of fair Asopia covers,
Laid in the tombs of heroes with their faces turned to the sunset,

He did, and taking as volunteers 500 young Athenians whose ancestors came from Salamis, was successful in capturing the island, that was to prove so important in later Athenian history. Solon never ceased to support and give credit to the oracle for its support in declaring the island was originally Ionian.

"Oracle" was the code name of a CIA project that the three founders (Ellison,
Miner, and Oates) had worked on together.

When CEO Lawrence J. Ellison and a few associates formed Oracle in 1977, they were out to prove wrong the prevailing theory that relationship databases could not be commercially viable.
Larry Ellison, Bob Miner and Ed Oates found Software Development Laboratories. Inspired by a research paper written in 1970 by an IBM researcher titled “A Relational Model of Data for Large Shared Data Banks”, the three decide to build a new type of database called a relational database system. Their original project is for the government and is titled Oracle. The founders believe that Oracle, meaning source of wisdom, would be an appropriate name for their project and receive permission from the CIA to use it.
What's in a name?
In 1978, Software Development Laboratories moved from their office in Santa Clara to a new one on Sand Hill Road in Menlo Park, the heart of Silicon Valley. In an attempt to explain what their company does, they changed their name to Relational Software Inc., or RSI. The newly-christened company shipped its first commercial SQL-based database, V2, in 1979 (V1 was never officially released). In 1982 RSI changed its name to Oracle Systems Corporation, which later become Oracle Corporation.