except it's weirder than that. i was watching an anime that used the word "hydra" at one point and the japanese pronunciation sounds like "hidora", so that was my first tip off to this connection- but you probably are wondering, why the "g" sound at the beginning?
the running theory is that they were using the russian for hydra, which is written Гидра, and pronounced like so: https://forvo.com/word/%D0%B3%D0%B8%D0%B4%D1%80%D0%B0/
the idea is that they used russian because part of the inspiration for the monster most likely comes from a japanese translation of the soviet fantasy film, Ilya Muromets specifically, the design and name appear to be inspired by the three headed dragon that shows up in the film. so, that seems like a pretty clear throughline- but to really drive home the connection, this dragon is called Zmey Gorynych, which was translated to "King Dragon" (or キング・ドラゴン). so they not only got inspiration for the monster design and the hydra name through this source, but this explains why Ghidorah is specifically King Ghidorah.
this tohokingdom thread seems to be one of the first places to popularize the connections: