From what I've read, the basic rule is that the name and number need to be easily readable.
If you have stripes, you either need a plain back or you stick a square on the back.
The exception to this is if the two colours of your stripes are similar in the colour spectrum, and they have ways of measuring this. I think this is why Bournemouth wouldn't need a plain back, as the contrast between a dark red and black isn't too bad. Blue and black stripes would be the same.
Some clubs get round this by having a different kit for the players and supporters, but I suspect this gets quite complicated as a lot of fans want names and numbers on their shirts