Link: https://youtu.be/Bj_eYIMDjlI?si=jQGltPuhJuH_AFm9
It comes from something my mam used to say when I was a kid. If someone was always complaining and miserable she would refer to them as "Grumbling Ginger". No idea why.
Anyway, at one time we had three people with red hair in the band so it seemed like an appropriately funny name!
Here's a link to a two-redhead version of the band! Original song written by my wife.