Princess Beatrice was reportedly supposed to have a different name. Her parents, Prince Andrew and Sarah Ferguson, the Duke and Duchess of York, didn't choose "Beatrice" and had another name in mind that Queen Elizabeth apparently rejected. 

According to reports, Prince Andrew and Fergie wanted to call Princess Beatrice as Annabel. However, Queen Elizabeth nixed the name and suggested Beatrice because Annabel sounded "too yuppie." 

Prince Andrew and Fergie apparently let the name Annabel slip in the media a few months before Princess Beatrice was born. However, they didn't officially announce her name until two weeks after she arrived in the world in August 1988. The press was reportedly surprised to learn that she would be actually called Beatrice when they knew as early as May that the Yorks wanted to name her Annabel. 

At that time of her birth, the two other popular royal names were Charlotte and Victoria. Beatrice, however, was also the name of Queen Victoria's youngest child, thus it was royal enough for Her Majesty.

Princess Beatrice's full name is Beatrice Elizabeth Mary, the last two serving as tributes to her grandmothers. The York royal also carries the title of "Princess" and is officially an HRH (Her Royal Highness) even though she isn't a working royal. Her sister, Princess Eugenie, also holds the same royal honor.

According to Daily Express, the York daughters were given royal titles by virtue of an order from the Queen's grandfather, King George V, from 1917, stating that the grandchildren of a sovereign's male heirs may hold royal titles. The York princesses' father, Prince Andrew, agreed to the titles.

On the other hand, Princess Anne's children, Peter and Zara, who are Princess Beatrice's cousins, don't technically get royal titles. The Queen, however, offered to give them one but their mother rejected this, opting to let Peter and Zara live as normal individuals.

Prince Edward's children, Louise and James, have titles as well, as their father is a male descendant. However, they are not known as princess or prince but Lady Louise and James, the Viscount Severn, as chosen by their father. 

Meanwhile, Princess Beatrice has been carrying on with her royal name as a private individual. But once she marries her fiancé Edo Mapelli Mozzi, the York royal could also inherit the title of countess by virtue of marriage since her husband was born into an Italian aristocratic family.