The Duke and Duchess of Cambridge have named their new baby Prince Louis Arthur Charles.The names honour both the Prince’s grandfather, Prince Charles, and Louis Mountbatten, the Duke of Edinburgh’s mentor who was killed by an IRA bomb in 1979.Prince George and Prince William both have Louis as middle names, with the announcement confounding bookies and experts who had believed it would not be repeated for the third baby Cambridge.Arthur had been the favourite predicted first name, eventually announced as a middle name. It is also one of the Duke of Cambridge’s own middle names.Kensington Palace said: “The Duke and Duchess of Cambridge are delighted to announce that they have named their son Louis Arthur Charles.”The baby will be known as His Royal Highness Prince Louis of Cambridge.” Asked about the baby’s name, she added tactfully: “The jury’s out on that one. I don’t know, we’re all just going to have to wait and see.” Asked how the Duchess and the baby were doing, Prince William said: “They’re very well thanks.”The now father of three said they are “in good form, luckily”, and added: “Sleeping’s going reasonably well so far, so he’s behaving himself which is good news.” Speaking for himself and the Duchess of Cornwall, presumably with a twinkle in his eye, he said: “We are both so pleased at the news. “It is a great joy to have another grandchild, the only trouble is I don’t know how I am going to keep up with them.”The Prince is now a grandfather to Prince George, four, Princess Charlotte, who will turn three on May 2, and the baby boy. Lord Louis Mountbatten pictured in 1977, two years before he was murdered by the IRACredit:PA The Duke and Duchess of Cambridge showing their third child to the world outside the Lindo Wing on MondayCredit:Karwai Tang /WireImage The Duchess of Cornwall also has five grandchildren who are regular visitors to their home, with the Prince said to delight in reading the youngsters stories. ‘Highlight of my career!’ The young Pc who took centre stage at baby’s first public outingThe baby joy extended not just to the Royal Family and avid monarchists. ‘I don’t know how I’ll keep up with them’, proud Prince of Wales jokesA delighted Prince of Wales welcomed the birth of his third grandchild, saying it was a “great joy”. The name is a significant tribute to the Royal Family, with the newborn Prince sharing names in common with his brother Prince George Alexander Louis, his father Prince William Arthur Philip Louis, and his grandfather Prince Charles Philip Arthur George.Kensington Palace announced the name of the Royal couple’s third child, who was born on Monday at 11.01am weighing 8lb 7oz.The Duke and Duchess will have shared the name with the Queen and the rest of their family before making it public. The Prince of Wales, who was on Tuesday travelling to France in time for a dawn service to commemorate the Battle of Villers-Bretonneux on Anzac Day, will pay his first visit to hold the baby on his return from duty.Other family members earlier remained tight-lipped about the baby’s name. The Countess of Wessex, who was conducting a string of engagements near Truro, Cornwall, said during a visit to Tregolls School on Tuesday: “I’m thrilled for them all, it’s lovely – really good news.” Pippa Middleton pictured leaving Kensington Palace on Tuesday afternoonCredit:Paul Grover for The Telegraph Since then, the Duke and Duchess have been kept busy settling in to life as a family of five at Kensington Palace.Born fifth in line, the baby is the Queen and Philip’s sixth great-grandchild and Kensington Palace said the couple, along with the Prince of Wales, the Duchess of Cornwall, Prince Harry, and the Middletons, were delighted with the news of the new arrival. The Duke of Cambridge holds up three fingers as he tells the media he has ‘thrice the worry now’ as he leaves the Lindo Wing Credit:BEN STANSALL /AFP New baby Louis evokes memories of Charles’ beloved uncle murdered by IRALouis was the first name of the Prince of Wales’ beloved great-uncle Earl Mountbatten of Burma.Charles will be touched that the Duke and Duchess of Cambridge decided to pay tribute to Lord Mountbatten, who was murdered by the IRA in 1979, by naming their son Prince Louis.The name, also one of Prince George’s middle names, is French and German in origin and means “renowned warrior”. Duke and Duchess settle into life as family of fiveAs the outside world clamoured for details, the Duke and Duchess appeared to simply get on with life: with two older children, even with the help of a nanny, they could hardly do less.The Duke, sporting a light stubble, was seen driving out of Kensington Palace on Tuesday afternoon, on an unidentified errand. Pippa Matthews, the first visitor seen driving into the Palace, spent several hours with her sister, the Duchess, and infant nephew before being photographed driving away. Parents Carole and Michael Middleton were unlikely to have been far away, famously supportive of the Duke and Duchess and their growing brood.Prince Harry and Meghan Markle, too, could surely not have kept away from joining the first eager visitors, living just next door and both adoring children.The Prince once called George and Charlotte “the most amazing things ever”.The Queen, who was in Windsor, is unlikely to meet her sixth great-grandchild imminently, with further duties at the castle on Wednesday, while the Duke of Edinburgh is recuperating privately from a hip replacement operation. Famous people named Louis include pop star Louis Tomlinson from One Direction and jazz trumpeter Louis Armstrong.Lord Louis Mountbatten was also the Duke of Edinburgh’s uncle and the brother of Philip’s mother Princess Alice.He was the last British Viceroy of India before independence in 1947.He was very close to Charles but Uncle Dickie, as he was known in the family, was assassinated by the IRA in August 1979.His boat was blown up on a fishing trip off the coast of County Sligo in the Republic of Ireland.Meeting the family: Auntie Pippa one first visitors at Kensington PalacePrince George and Princess Charlotte had already been introduced to the new baby at St Mary’s Hospital and were likely being eased into their new roles as big brother and middle sister in their own home on Tuesday. Royal Collection releases official souvenirs before baby’s name announcedThe official commemorative souvenirs marking the birth of the Duke and Duchess of Cambridge’s baby son have gone on sale – before the new prince’s name had been announced.Featuring a lion cub and unicorn inspired by the Royal Arms, the Royal Collection china is decorated with gold ribbons, silver pompoms and a coronet-inspired pattern.The pieces bear the words “Welcome to our new royal baby” and display William and Kate’s coronet. Louis was the 71st most popular name in England and Wales, according to the latest available figures from the Office for National Statistics.In 2016, just 911 boys were given the name Louis in England and Wales.It was more popular in the early 2000s when it ranked around 39th, but was not popular throughout the 20th century.Louis has been the name of many rulers across the world, including 18 kings of France. The Royal couple introduced two new members to the family today…. An honour and utter privilege to have been the ‘Door Officer’ for the birth of Their Royal Highnesses new baby boy! Today was an amazing day and a highlight of my career! #RoyalBaby3 #RoyalBaby3 #RoyalBaby pic.twitter.com/md6kMw3WSs— PC Tyler O’Hare (@TylerOHare) April 23, 2018 Prince William leaves Kensington Palace by car on Tuesday afternoonCredit:Jack Taylor /Getty Sophie, Countess of Wessex meets pupils during a visit to a school in Truro on TuesdayCredit:Cornwall Live / SWNS.com Prince William greets his brother Harry’s fiancee Meghan Markle as they arrive for an Anzac Day service at Westminster Abbey Credit:HANNAH MCKAY /Reuters The Prince of Wales already has two grandchildren in Prince George and Princess Charlotte, pictured arriving at the Lindo WingCredit:DANIEL LEAL-OLIVAS /AFP Abbey bells and gun salutes mark Royal birthOfficial celebrations were already under way, with the bells of Westminster Abbey ringing out from 1pm and gun salutes fired in London at 2pm.The soldiers, horses and Guns of The King’s Troop Royal Horse Artillery rode out from Wellington Barracks into Hyde Park for a 41 round salute, and the Honourable Artillery Company (HAC), the City of London’s Army Reserve regiment, fired a 62-round Gun Salute from The Tower of London.Video: Moment royal birth was marked by gun salutes Video: New Prince of Cambridge’s first public outing The official range includes a pillbox costing £35, a tankard for £39 and a plate priced at £49.Each item in the range is gilded with 22-carat gold and made in Stoke-on-Trent using traditional methods.There is also a pram-shaped woven decoration, made with glistening threads, delicate pearl detail, and embroidered on the back with “Royal Baby 2018”, for £14.95. A young Metropolitan Police constable, Tyler O’Hare, who took centre stage during the Royal baby’s first public appearance outside the Lindo Wing was also celebrating.Sharing pictures of himself sternly keeping them safe by standing guard, he wrote on Twitter: “An honour and utter privilege to have been the ‘Door Officer’ for the birth of Their Royal Highnesses new baby boy!“Today was an amazing day and a highlight of my career!” The range of official commemorative chinaware to celebrate the prince’s birth Credit:Royal Collection Trust The announcement had been eagerly anticipated since the couple showed off their new son to the world on the steps of the exclusive maternity unit, the Lindo Wing, on Monday evening. The Queen horse riding at Windsor on Monday before the latest Royal baby was bornCredit:Kelvin Bruce Prince William: ‘Sleeping’s going reasonably well so far, so he’s behaving himself’The Duke of Cambridge joined his brother Prince Harry and soon-to-be sister-in-law Meghan Markle at Westminster Abbey for an Anzac Day service on Wednesday afternoon.But the topic of conversation quickly turned to the new Prince. The Prince’s words chimed perfectly with those of his son the Duke, who had held up three fingers – one for each of his children – when departing from hospital and laughed that he had “thrice the worry now”. Want the best of The Telegraph direct to your email and WhatsApp? Sign up to our free twice-daily Front Page newsletter and new audio briefings.