What is the HD re-release of Rayman 3: Hoodlum Havoc called?

The HD re-release of Rayman 3: Hoodlum Havoc is called Rayman 3 HD.

Rayman 3: Hoodlum Havoc originally launched in 2003 for platforms including PlayStation 2, Xbox, GameCube and Windows. The HD edition arrived digitally for PlayStation 3 and Xbox 360 on March 21, 2012, updating the presentation for high-definition displays.

Rayman 3 HD is an enhanced re-release rather than a new numbered sequel. Its most visible changes include widescreen high-definition visuals and subtitles for the game's dialogue, while the core adventure remains Rayman's battle against André, the Black Lums and the Hoodlum army.

The alternatives are easy to mix up because the series has several similarly named ports. Rayman Advance is a Game Boy Advance version of the original Rayman, Rayman Revolution is an expanded PlayStation 2 version of Rayman 2, and Rayman 3D is a Nintendo 3DS port of Rayman 2: The Great Escape.