The band's lead singer is Maynard James Keenan, and that band is Tool.
Keenan co-founded Tool in Los Angeles in 1990 after meeting guitarist Adam Jones. The band's core lineup became Keenan, Jones, drummer Danny Carey and bassist Paul D'Amour, with Justin Chancellor replacing D'Amour in 1995. Keenan's dramatic vocals and cryptic lyrics became a defining part of Tool's alternative-metal sound.
Tool released its debut album, Undertow, in 1993, followed by Ænima, Lateralus, 10,000 Days and Fear Inoculum. The band is known for lengthy compositions, unusual time signatures and visual artwork created in collaboration with artist Alex Grey and others.
The main source of confusion is that Keenan also sings for A Perfect Circle and Puscifer. Those are separate projects, not alternate names for Tool. A Perfect Circle began in the late 1990s with guitarist Billy Howerdel, while Puscifer is Keenan's more experimental solo-led project. His association with all three groups makes Tool the canonical answer to this question, but not his only band.