Where did the name "Deep Purple" come from?

On the boat between England and Denmark, Ritchie Blackmore and bassist Nick Simper were interviewed about the new band. It seemed that it actually was during this interview that the band changed it's name to Deep Purple - named after an old song that was a favourite of Ritchie's granny, or something like that. According to an interview with Nick Simper in an old issue of Darker than Blue, the journalist asked them what the name of the band was. Ritchie looked at Nick with a grin, and said "It's Deep Purple". Nick smiled back, and that was it.

I think the song below might be it:

Deep Purple

When the deep purple falls
over sleepy garden walls
and the stars begin to flicker in the sky
thru the mist of a memory
you wander back to me
breathing my name with a sigh.

In the still of the night
once again I hold you tight.
Tho' you're gone your love lives on when moonlight beams
and as long as my heart will beat,
lover, we'll always meet
here in my deep purple dreams.

- Mitchell Parish