Absolutely named for Earl Louis Mountbatten, who was Charles favorite uncle, but also Prince Philip's uncle and guardian (technically he was Prince Charles' great-uncle on the Mountbatten side. He was also a cousin of Queen Elizabeth on the Windsor side, 4th or 5th cousin, I believe, but don't quote me on that part.) I actually was rather sure that they would name the baby Louis; I had heard that because of Prince Philip's declining health, that the Queen wanted to please him in the choice of a name, and this one definitely would have been at the top of his list.
Louis Mountbatten had TREMENDOUS influence on the British royal family after the death of George VI; some people even say that he took it to Machiavellian levels. He wanted Charles to marry his granddaughter Amanda Knatchbull, and Charles dutifully proposed; but thankfully Amanda turned him down; they really were far too closely related to for marriage to be a good idea.
His assassination made the family even more determined to remember him as a saint. He *was* a brilliant man, no question, but history tells us that a saint he was not.
PS: Louise has been a favorite name in the royal family since long before the Battenburgs became the Mountbattens. The most famous of them was Queen Victoria's youngest daughter, who became the Duchess of Argyle. She was a talented artist, a tremendously well-loved patron of the arts and a tireless patron of charities. She was also a well-known crusader for the education of women. Anne, the Princess Royal, also has Louise as one of her names. (She is Anne Elizabeth Alice Louise.)