I've also never seen 'Painted Wolf' as the main common name, though you sometimes see it given as a translation of the scientific name. I'd have said the most common name used was African Wild Dog (this is the name I tend to use).
yes, to be fair African Wild Dog is probably now the most common usage. I think 'Painted Wolves/Dogs' was originally used in T.V. documentary titles and some zoos may have cribbed it- e.g. Yorkshire WP call them 'Painted' Hunting Dog.
Also interesting to note that Whipsnade, where this Gallery photo of the Cranes was taken (link, link), was at one time-1950/60's era, the only UK collection with a small group of Hunting Dogs(ZSL may have had one or two on show at the same time). Yet in recent years they have become more widespread in our zoos and are even in a Safari Park now too.
They have been called Japanese over the years, and I believe have quite a role in Japanese art & culture. To me, 'Japanese' is as good as 'Manchurian'; 'Red-crowned' suggests a totally inappropriate association with Balearica.