Singapore was only called this for a short time. This was during WWII when the Japanese conquered and occupied the island. Syonan-to (also can be Romanized as Shonan-to) is made up of three Chinese characters. They are 昭南島.
These characters have often been translated as meaning "Light of the South Island." However, this is not the best translation. The first character does mean "light" or "shining," but it is also the first character in the reign name of the Showa Emperor. The second character means "south" and the third means "island." The better translation of this is something like "Southern Island Taken in the Showa Period."
In other words, Syonan-to is something of an abbreviation for a longer Japanese phrase that would be unwieldy as a name.