Gongen (権現)
Gongen is a kind of Japanese shingo (the title given to a Shinto shrine). The concept of gongen is based on Honji-suijaku setsu, which is the theory that the Japanese Shinto deities are recognized as manifestations of the original Buddhist divinities.
Gon' (as a Chinese character, '権') means 'temporary' or 'provisional,' as is used in the words 'Gon Dainagon' (provisional major counselor), and 'gen' (or '現') means 'manifestation,' and therefore 'gongen' literally means the Buddhist divinity's manifestation in the form of a provisional deity.
Summary
Gongen is shingo, so it is mostly used as the title of the deity to which a specific shrine is dedicated and linked, while it rarely implies the deity as separated from the shrine.
For example, 'Amenokoyane no Mikoto' (a legendary ancestral deity) is also called 'Kasuga Gongen,' because Kasuga-jinja (or Kasuga-taisha) Shrine is dedicated to 'Amenokoyane no Mikoto.'
The deity itself is, however, not called 'Amenokoyane Gongen.'
Some shrines each have their own title for gongen, even though these are dedicated to the same deity. This might suggest that the title of gongen is given by the shrine.
In fact, 'gongen' is often used as the title of a shrine too, as is the case with 'Kasuga Gongen.'
Moreover, the name of the place in which the shrine is situated is often incorporated into the enshrined deity's name, as is the case with 'Nikko Gongen' (the deity to which Nikko Futarasan-jinja Shrine, situated in Nikko City, Tochigi Prefecture, is dedicated), and a shrine's name itself often comes from a place name.
Besides, there are cases in which the number of deities to which a shrine is dedicated is attached to the title of gongen, as is the case of 'Rokusho Gongen' (Six Deities' Gongen); in this case, the six deities are taken as a group. Occasionally, the place name and the number of deities are both attached to the title of gongen, as is the case of 'Nikko Sansho Gongen' (Nikko Three Deities Gongen). One can find cases in which the name of suijakushin (the provisional Shinto deity) is derived from the name Honji-butsu (the original Buddhist divinity), as is the case with 'Zao Gongen' (Avatar Zao) derived from 'Zao Bosatsu' (Zao Bodhisattva), but such cases are rare. The descriptions above of the title of gongen are mostly true of the title of myojin (the illuminator deity).
Others
Owing to the government policy of the separation of Buddhism and Shintoism in the early Meiji period, the use of the title of gongen was banned for some time in order to deny Honji-suijaku setsu, but eventually the ban was withdrawn.