Name of the band

The name "Gentle Giant" was coined by Colin Richardson, a "wordsmith" who worked for Gerry Bron, the manager of Simon Dupree and the Big Sound. According to an interview in LouderSound:

It was Bron, too, who was instrumental in their new name: “Colin Richardson, a wordsmith who worked for Gerry, titled us,” Phil recalls. “‘You play gently and you play loud: Gentle Giant.’ At first I cringed: it sounded like someone selling sweetcorn.”

“We were putting the music together,” Derek says. “We said, ‘Call us what you like!’”

Thanks to eagle-eyed fan Luke Manning for locating this information.

Other sources

In Proclamation number 4, page 49, Gary Green says that the name "Gentle Giant" was invented by "Colin somebody."