Something borrowed from an English king, something the shade of Saltire blue, something traditionally Windsor or Spencer, and something new--to the Royal Family:
Something borrowed: A given name from the British Royal's family tree that is generations removed from current family members with one notable exception--Elizabeth--if the baby is a girl. Thus, if the child is a boy, forget Charles, Andrew, Edward, Harry, William, James, and Phillip The Cambridges also won't choose John because of its association with John Lackland. Looking at a list of English sovereigns, this leaves Richard.
For girls, Sophie, Anne, Beatrice, Katherine, Beatrice, and Eugenia are out as first names, although Elizabeth and Victoria are keepers.
For a second given name Prince William and the Duchess of Cambridge might choose a name that brings to mind Scottish kings: Think Robert the Bruce, Alexander, and David, which also refers to the patron saint of Wales, for boys and Margaret for a wee lass. Mary, however, has some unpleasant associations--notably Mary Tudor, although Mary Stuart was beheaded for treason by Elizabeth I.
For a third name, look for a family name used by either the Windsors of the Spencers: Albert or the male version of one of Diana's middle names, Francis. For a future queen, look for Diana or Frances to appear in this position.
Something new--at least for the Royal family--from the Middleton clan: Michael for boys and a royal variation of Carole--Caroline or Charlotte, although Katherine might appear here.
Thus, an appropriate name for a male heir to the throne might be Richard Robert Francis Michael and a suitable name for a future queen might be Victoria Margaret Frances Caroline.
Then again, the Cambridges might throw a suitable combination of names in a hat. After all, the child won't have to be called by his or her first name.