Beni shōga
Beni shōga (紅生姜) is a type of tsukemono (Japanese pickle). It is made from ginger cut into thin strips, colored red, and pickled in umezu (梅酢), the pickling solution used to make umeboshi; the red color is derived from red perilla. It is served with very many Japanese dishes, including gyūdon, okonomiyaki, and yakisoba.
Beni shoga is quite easy to find in 10-12 Oz. Jars, which can be very expensive. It is almost impossible to find in larger packages.
Beni shōga is not the pickled ginger served with sushi, which is called gari.