There are quite a number of animals that feed on "filth", many of which live alongside us and, indeed, eat dead skin cells, hair, and other waste lying around and prevent it from building up. We call these "detritovores", and examples include dust mites, millipedes, flies, woodlice, slugs, and worms. However, such animals tend to be small and have a generally low-energy lifestyle. It's hard to think of why such a creature would be humanoid.
However, it is worth noting that modern humans produce a lot of still-edible organic waste, which is why scavengers like rats and raccoons tend to congregate in human cities. I would guess that the Akaname evolved from such a creature, growing more tolerant of toxins in order to exploit a niche that their garbage-raiding cousins could not.
If you want a darker possibility, perhaps in a far-future dystopian setting where the divide between the rich and the poor has grown, and the children of the poor have no chance of rising beyond their social class, thousands of generations of poor humans could evolve to live off of more and more meager fare until even bathroom filth becomes a usable food source.
In either case, the creature would likely have a lower-energy lifestyle and greatly reduced intelligence compared to the species it evolved from. Living off of even the most base of resources means the Akaname doesn't have a lot of energy to spare, but being able to eat almost anything means it doesn't really need a lot of brains to get by.