The whole deal with the names is weird given that poseidon is the only one of the 3 thats not Roman name... Neptune a normal merman is the Roman name of the god of the sea

Pluton (or rather, Plouton) is actually Greek, and was an alternate name for Hades (though Hades was also used as a name for the realm of the dead, while Plouton referred only to the god and not to his domain). The Romans later latinized it to Pluto.