It appears to be a reference to Lord Louis Mountbatten, an uncle of Prince Philip, the Duke of Edinburgh and a second cousin to the Queen. He was a commander during WWII and first Governor General of India. His maternal grandfather was also called Prince Louis Alexander of Battenberg.
Prince William's full name is William Arthur Philip Louis. Prince George's full name is George Alexander Louis.
The inclusion of Charles also matches the trend for Princess Charlotte, whose full name is Charlotte Elizabeth Diana.
Prior to the big reveal, the name Arthur was the frontrunner with UK bookies, with Albert, Fred and Philip also popular bets. Louis was an outside choice at 18/1.
The name is more popular with royalty in France, where 18 kings have been named Louis, including Louis IX, who led two crusades, and Louis XIV, the Sun King, who ruled France at the height of its power, built the Palace of Versailles, and the longest reigning monarch in the history of Europe.
Kate gave birth on Monday at 11.01am on April 23, in the Lindo Wing at St Mary's Hospital in London with her husband Prince William by her side.
The royal couple followed the tradition observed with their previous children of waiting to reveal the name to the public, in order for them to inform the Queen first.
It's a long-established custom: Prince William's name was not announced for a week when he was born, while his father Charles' wasn't known for a whole month. While Prince George and Princess Charlotte took two days each to become known, the world was waiting four days to find out about Prince Louis.