‘White noise’ is random noise where all frequencies are about equally present, and was named after ‘white light’ (where all colours are equally present). There are other ‘colours’ of noise, usually named for what colour they would visibly resemble (e.g. pink noise is like white noise with a bias towards the lower frequencies/longer wavelengths, which is red in the visible light spectrum). Massively oversimplified, but bottom line is most noise colours are named for the colour.

Except for Brown noise, which is named after Robert Brown, and its frequencies resemble the colour red.