Kyogre did not originate from fanon, and the information on this page may not be entirely accurate to their canon. You may read more about this subject in the context of their canon on the following wiki(s):
Kyogre, known in Japan as カイオーガ (Kaiorga), is a Legendary Water-typePokémon. Kyogre is known for its ability to expand the sea, and has feuded against Groudon in ancient times. Together with Groudon and Rayquaza, it forms a trio of super-ancient Pokémon, each hailing and guarding one respective type of elemental sphere (Kyogre's being the hydrosphere).
Kyogre can undergo through Primal Reversion, to become Primal Kyogre using the Blue Orb, which is said to be its original form.
Kyogre is a massive cetacean Pokémon with two large pectoral fins from its side, each with four square-shaped tips, as if they were fingers. Its body is deep blue and its lower jaw is colored white and has two spikes protruding under it. Above each of its eyes are two white, ovarian spots. Its eyes have a yellow sclera and placed in a black area, rimmed with a red line. Red lines also rim its chin, dorsal fin and torso, and the markings on its pectoral fins are also red. All these red stripes will glow when Kyogre brims with power. On the abdomen on its underside are two white stripes. Its tail fin is split up in four tattered parts, two of them on each side and the inner parts smaller than the outer parts.
Kyogre has full control over the water of the Pokémon world, and has the ability to expand the ocean. It has the ability to cover the entire sky with dark rain clouds, even with the harshest sunlight, and filling entire areas with downpours of rain. Because of this, Kyogre is seen as a savior by the people that suffered from incredibly long droughts, but can also be seen as a pest by the people suffering from massive rain floods. It is the opposite of Groudon, who it fought against long ago. After this eternal battle, Kyogre went to a trench at the bottom of the ocean to rest for ages.
When Primal Reversed, Kyogre's size has been more than doubled. Its body becomes navy and most of the red lines on its body become bright blue. Its sclera has become orange, it pupils glow red and the holes where the eyes were located in glow yellow. The white spots above its eyes have become a pearlescent gold, which emit light. This same beautiful, translucent color also fills in the red and blue patterns on its pectoral fins, and lines on the tattered tail fins and its back. Kyogre's forehead gains a pattern of the same colors - this pattern resembles an uppercase Alpha. The patterns on its pectoral fins resemble lowercase Alphas.
This appears to be Kyogre's original form when it feuded against Groudon centuries ago. It is filled with an energy that spills forth as seawater, and it appears its body composes almost completely out of water. It can attack its opponents by raising large pillars of water from above.
In this form, Kyogre battled Groudon for ages and ages, as both of them wanted more and more energy for itself. As they already have strong natural energy in possession, each of their duels brought the inhabitants of Hoenn in danger every time, and the people of their time called Primal Kyogre and its rival tormentors.
Kyogre is most likely based on the sea master Leviathan, of Hebrew legends, which counterparts, Behemoth and Ziz, mirror Kyogre's counterparts, Groudon and Rayquaza. While Kyogre doesn't resemble the traditional depiction of Leviathan, who seems to be a serpentine sea dragon, the word "Leviathan" is modern Hebrew for "whale", a creature which Kyogre's appearance does seem inspired after, especially orcas.
Kyogre and Kaiorga may be a comination of 海 kai (ocean), and either orca (the official name of the killer whale) or ogre. It may also involve 海王 kaiō (king of the sea), which is derived from 海王星 Kaiōsei (Neptune).