Hanako to Guuwa no Teller (2003)

Blurb:
The "No-mouth Woman," "The Man Under the Bed," and the "Human Faced Fish" are supposedly urban legends. But what few people know is that just at the moment when someone believes them to be true, they become reality and appear before them! Enter Daisuke Asou, a folklore detective who deals with such cases. He calls these fantastic creatures "allegories." What’s a folklore detective to do?

Source: www.anisearch.com/manga/4076