They will keep the baby's name Royal, especially since it is the Future monarch.
No names from Kate's family. So that means no Carole (maybe even Caroline) , Philippa, Michael and James, even if they may also be used by actual Royals as well.
No Diana, she wasn't a Royal, as much as everyone would love William and Kate to name a daughter after Diana, they most likely won't, William will want people to remember his mother as the only Princess Diana (even thought she never held that title she was know as that) rather than people having to say which Diana they are talking about, when you hear Princess Diana you will think of Williams Mother, if there are two Princess Dianas, Diana Spencer may get overshadowed by her Granddaughter.
Diana's middle name was Frances, it was so her mothers first name (Williams other Granny), as well as many of Diana's ancestors, the Queens Great Grandfather was also Frances, Queen Victoria had many male Ancestors named Francis, so that may be a middle name possibility for either Boy or Girl.
A middle name for a girl I think may be Elizabeth, seem the baby will be born in the 60th year since Queen Elizabeth's Coronation (she became Queen in 1952 when her father died but didn't have her Coronation until the following year 1953) also Kate's middle name is Elizabeth, Kate's mother has it as her middle name too, The Queens second Great Granddaughters middle name is Elizabeth, aswell as many of Williams Royal relatives bare that name as one if their middle names.
CLOSE LIVING TITLES RELATIVES OF WILLIAM
Elizabeth - Queen Elizabeth (Williams Granny)
Anne - Princess Anne (Williams Aunt)
Beatrice - Princess Beatrice of York (Williams Cousin)
Eugenie - Princess Eugenie of York (Williams Cousin)
Louise - Lady Louise Mountbatten-Windsor (Williams Cousin, Should be Princess Louise)
Alexandra - Princess Alexandra of Kent (Both Queen Elizabeth and Prince Philips first cousin)
Philip - Prince Philip, Duke of Edinburgh (Williams Grandpa)
Charles - Prince Charles, Prince of Wales (Williams Father)
Henry - Prince Henry 'Harry' of Wales (Williams Brother)
Andrew - Prince Andrew, Duke of York (Williams Uncle)
Edward - Prince Edward, Earl of Wessex (Williams Uncle)
James - James Mountbatten-Windsor, Viscount Severn (Williams Cousin, Should be Prince James)
Edward -Prince Edward, Duke of Kent (both The Queen and Prince Philips first cousin)
Michael - Prince Michael of Kent (both Queen Elizabeth and Prince Philips first cousin)
Richard - Prince Richard, Duke of Gloucester ( The Queens first cousin) (Richard had a Brother called William who died in the 70's)
OTHER RELATIVES OF WILLIAM
Zara - Zara (Philips) Tindall (Williams Cousin)
Savannah - Savannah Philips (Williams Cousins Daughter, The Queens Great Granddaughter)
Isla Elizabeth - Isla Elizabeth Philips (Williams Cousins Daughter, The Queens Great Granddaughter)
Sophie - Countess of Wessex (Married the Earl of Wessex)
Sarah - (was married to the Duke of York)
Sarah - Lady Sarah Chatto (Princess Margaret's daughter)
Margarita - Margarita Armstrong-Jones (Princess Margaret's Granddaughter)
Peter - Peter Philips (Williams Cousin)
David - David Armstrong-Jones (Princess Margaret's Son)
Charles - Charles Armstrong-Jones (Princess Margaret's Grandson)
Arthur - Arthur Chatto (Princess Margaret's Grandson)
Samuel - Samuel Chatto (Princess Margaret's Grandson)
DIANA'S BROTHER, EARL SPENCER'S CHILDREN
Kitty Eleanor Spencer
Eliza Victoria Spencer
Louis John Spencer
Edmund Charles Spencer
Lara Caroline Spencer
Charlotte Diana Spencer
ROYAL ANCESTORS OF THE BABY
CURRENT MONARCHS AND HEIRS
Fredrick of Denmark
Christian of Denmark
(Male Heirs to the Throne of Denmark have been called Fredrick and Christian alternating for 100's of years, so I'm sure William won't use one of them)
Philippe of Belgium
Elisabeth of Belgium
Willem-Alexandre of The Neatherlands
Catharina-Amalia of The Neatherlands
Haakon of Norway
Ingrid-Alexandra of Norway
King Juan Carlos (John Charles in English)
Felipe of Spain
Leonor of Spain
King Carl Gustaf
Victoria of Sweden
Estelle of Sweden
PAST BRITISH MONARCHS
William I, II, III, IV
Henry I, II, II, IV, V, VI, VII, VIII
Richard I, II, III
Edward I, II, III, IV, V, VI, VII, VIII
Mary I, II
Elizabeth I, II
James I, II
Charles I, II
George I, II, III, IV, V, VI
I think they will name it something Traditional that sounds Modern, I like Louis and Edmund, although Diana's Brother (Williams Uncle) has two sons with these names, they are not Royal Children so I don't think this will affect Williams Child.
George is a 'very close to the Queens heart' name that hasn't been used in a while
(The Queens Father was King George VII, although his name was Albert and nickname was Bertie).
They won't use Albert as a first name, even though Queen Victoria stated she wanted all future Monarchs have a double Barrelled First name with Albert at the front, her oldest son and heir was Albert-Edward and his son was Albert-Victor, when Albert-Edward became King he chose to just be King Edward VII, as he wanted people to remember his father as the only Albert, his son Albert-Victor died before becoming King and so Albert-Edwards younger son George became King George V, he is our Queens grandfather (if Albert-Victor hasn't died we wouldn't be having this conversation lol).
Also Prince Albert is a disgusting male lower body piercing.
People have mentioned John, although it has been used for past Kings and Princes, it is now unlucky to the British Royal Family and they don't use it, all Princes names John have died young or had problems, The last Prince name John died at Birth and the John before him died in childhood due to Epilepsy, Diana originally wanted William to be named John after her Father but the Royals wouldn't allow it.
For a girl I like Alice, it sounds modern, its cute and is also the name of Prince Philips Mother, also the name of Queen Victorias second daughter, although Queen Alice doesn't sound quite right to me.
Victoria is also a great middle name choice as Queen Victoria stated she wanted all of her Female decedents to have Victoria in their names in honour of her, most of her Granddaughters and Great Granddaughters had it in their names, Princess Eugenie of York (The Queens Granddaughter) is the first British Royal to have Victoria in their name for a long time, it won't be a first name as the current Crown Princess of Sweden is called Victoria, she will soon be Queen Victoria of Sweden, a British Queen Victoria is also a lot to live up to and the Future Queen 'Victoria II' would eventually be overshadowed by her ancestor Queen Victoria I.
Although there is a current British Princess Alexandra, I think it sounds great, it's very Royal, Fashionable and has lots of nickname possibilities, like Alex, Alexa and Lexie. It was the name of Queen Victorias son, Edward VII's wife, she was born Princess Alexandra of Denmark and later became Queen Alexandra.
They could also use Alexandrina, as that was Queen Victoria's middle name.
Other Consorts with modern sounding names have been Queen Charlotte and Queen Sophia, although Sofía is the current consort to the King of Spain and is also the name of their Granddaughter, Infanta Sofía.
Other Royal Ancestors of Queen Victoria with unique sounding names have been;
Dorothea, Augusta, Magdalena, Éléonore, Christiane Emilie, Theodora, Henriette, Sophie Antoinette.
August, Augustus, Ernest, Heinrich, Francis Josias, Ferdinand.
Although it doesn't sound very Royal, Queen Victoria loved the name 'Feodora' and in a letter to her daughter she said she hoped it would be used more often.
Sorry for my rambling, I didn't realise I wrote so much.