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About
A Hideo Kojima Game is a brand name on the box cover and titles of video games that were directed by famed game designer Hideo Kojima. The brand gained notability online after video game publisher Konami removed Kojima’s name from his studio, the box cover and all promotional ads for Metal Gear Soild V: The Phantom Pain as part of the rumored fracture between the two.
Origin
On March 19th, 2015, several gaming news sites including Kotaku,[1] PC Gamer,[4] Polygon,[5] and Eurogamer[6] reported about the rumor that Hideo Kojima might be leaving Konami, among the evidence include the renaming of Kojima Productions Los Angeles into Konami Los Angeles Studio and the removal of Hideo Kojima’s name from Metal Gear Solid V: The Phantom Pain’s title on the official Konami website (shown below, top was before the change).

On July 14th, 2015, a NeoGAF thread was submitted by user Love Deterrence that shows the final version of the official box art for Metal Gear Solid V: The Phantom Pain which reveals Kojima’s brand being completely removed.[7]
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External References
[1]Kotaku – Why People Think Hideo Kojima Is No Longer At Konami
[2]Wayback Machine – The MGSV site before the change
[3]Konami – The MGSV site after the change
[4]PC Gamer – Kojima name vanishes from Metal Gear Solid 5 materials
[5]Polygon – Konami removes Kojima name from Metal Gear games, Kojima rumored to leave
[6]Eurogamer – Hideo Kojima’s name removed from Metal Gear Solid 5 branding
[7]NeoGAF – Metal Gear Solid V final box art