Yes, some chickens are like that.
And just like the dogs, the mixed chickens are given quite a variety of names.
For example, there is one general kind that can be called Red Sexlinks (females are red, their brothers are a different color.) They get sold as ISA Brown, and Golden Comet, and Red Star, and about ten other names.
I grant the names don't get mixed very much, unlike dog breeds, but hatcheries do keep making up names for new mixes, and they can get really hard to keep track of.
I know what Red Sexlinks are (red female chickens, with their brothers being a different color, so you can tell from the time they hatch.) But I get confused when they also appear as Red Stars and ISA Browns and Golden Comets (but not Production Reds because those are not color sexable, and not Starlight Green Eggers because those lay green eggs while the other ones lay brown eggs.)
Sapphire Gems and Blue Stars have blue feathers and lay brown eggs, while Prairie Bluebell Eggers have any color feathers but are supposed to lay blue eggs.
Actually, "Australorp" is almost an example of a combined name: descended from Opringtons in Australia.
