His name is taken from the ancient Roman god of the sea, Neptune. Often, his name---or that of his namesake---is used in expressions indicating divinity, such as "By Neptune!" or "Neptune preserve her!" This and his apparent powers imply Neptune is supposed to be a god rather than simply a king, although it has never been proved that any of the Bikini Bottomites worship him at all.
King Neptune lives in Atlantis, where his palace stands. However, in both appearances his palace has made, they are both different in appearance. In "Neptune's Spatula," the palace is described to be far away from Bikini Bottom. In the movie, the palace is just outside of Bikini Bottom borders. This could indicate that the Palace was moved from Atlantis to nearby Bikini Bottom. The indication that the Movie takes place after the actual series can also be supported by this.