Princess Beatrice of York, the eldest child of Prince Andrew and Sarah Ferguson, has been a member of the royal family from birth. But, Beatrice won’t ever be addressed as a Duchess, and she won’t adopt her father’s status to succeed him as the Duchess of York, unlike other members of the Royal Family.
Due to the fact that the Dukedom of York, like the other royal dukedoms, may only be carried on to a male heir. Prince Andrew has two daughters which means he has no male heir.

Andrew’s title will return to the Crown upon his death. Because of this reason, Beatrice will never be recognised as the Duchess of York like her mother is right now.
Princess Eugenie and Princess Beatrice did not receive a new royal title when they were married, as is customary for members of the Queen’s family.

Princess Margaret, a sister of the Queen, wed Antony Armstrong-Jones in 1960. The Queen later gave Antony the Earldom of Snowdon, elevating Margaret to the rank of Countess.
However, neither Edoardo Mapelli Mozzi, Beatrice’s husband, nor Eugenie’s spouse Jack Brooksbank earned a title after their weddings in 2018 or 2020, respectively.
Although she doesn’t use it in public, Beatrice does has an Italian noble title as a result of her marriage to Edoardo.
In a prior interview with the Daily Mail, Edoardo’s father stated:
“Edoardo is the only male descendent taking the family into the next generation.
“He is a Count – his wife will be a Countess automatically and any of their children will be counts or nobile donna.”
Since the daughter of Beatrice and Edoardo was born last year without any royal titles, she is referred to as Miss Sienna Elizabeth Mapelli Mozzi.

Why is Princess Beatrice called an HRH?
HRH is a title that means His Royal Highness. Children born into the male line of a Monarch are naturally HRHs. This rule comes under the Letters Patent issued in 1917 by King George V. So, the only daughter of Elizabeth II, Princess Anne, could not make that claim for her offspring, but all of The Queen’s sons could.
Therefore, all of Prince Andrew’s offspring would be eligible for HRH and Prince or Princess titles because he is the monarch’s second son. That’s why Princess Beatrice has the title of HRH.