There's an interesting story tied up with the name of this band.
It came from a Monty Python sketch, yes, but more specifically, it came from one called "Rock Notes" which was basically a call-in show about the latest bands. All of the bands have silly names, but "Toad the Wet Sprocket" is the silliest. Apparently, the Monty Python members tried to come up with a name so obtuse that it would never, ever be the name of a real band.
According to Eric Idle, when he heard of the actual band on the radio, he nearly drove his car off the road.
Also: According to user atlas, Philips performed part of the Rock Notes sketch with a friend in high school and fell in love with the name then.
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