One or two films have featured them as 'Painted Wolves' a rather fanciful name which maybe is the root of the name change. Or does the Latin name Lycaon pictus refer to it? (I don't know)
Give me 'Hunting Dog' anytime- that is what they are and that's what they do..
Lycaon pictus does indeed mean 'painted wolf'.
I believe Hix is bang on the money - this was a PR job, mostly to improve the animals standing in it's home range ('Hunting' dogs not popular with farmers, 'wild' dogs has associations with strays). It has spread to zoos from in situ conservation projects, I believe.
But 'Painted Dog' is not a name I'd ever use.