I think there was a "dislike" from the name Albert among Victoria's children, only they were forced to use them after the matriarch imposition.
Edward VII was known as Bertie but he refused to reign as Albert I.
His elder son Albert-Victor Duke of Clarence was known as Eddie - ok not to be confused with his father. Would he have reigned as Albert should he have succeeded his father, knowing the latter had refused the name ?
Edward VIII was always known as David, but choose to reign with his 1st name in honour of his grand-father.
By the time G VI succeeded his brother, nobody could foresee a king Albert coming whatever the circumstances.
British royalty are too traditionalist to innovate in matters of name, and Victoria was the latter to have a never used before name.
I recall when Pss Elizabeth was asked under which name she would reign, she looked surprised with the question and replied: Elizabeth, of course.
Being named Elizabeth Alexandra Mary, I guess the only other option would have been Mary, Queen Mary III.
It is often down to circumstances.
For instance George VI had George as one of his names but was known as Bertie from his first name Albert until his succession. Had he succeeded without the succession crisis (possibly like his father due to the early demise of his older brother) we might have seen a King Albert I.
Why Victoria chose to reign under her second name i don't know. As far as i know she was known in the family as Drina from Alexandrine. That name was in honour of Tsar Alexander I of Russia. However i believe she was styled as HRH princess Victoria of Kent before her succession so that name seems to have been her public name.
The late princess Christina of the Netherlands was baptised Maria Christina and known as Marijke for most of her childhood. She herself preferred her second name over the name she grew up with and started using her second name.
Princess Laurentien of the Netherlands is officially Petra Laurentien but i believe she always used her second name.
King Willem-Alexander of the Netherlands is known as Alexander to his family but opted to keep his full hyphenated first name as a regal name but did not want to be Willem IV or Willem IV Alexander. He made some stupid remark about Willem IV being in the field with Bertha XXXVII and linking numbers to cows. Not very nice if you consider that most of his reigning relatives and friends do have a regnal number.
The princess of Orange is officially Catharina-Amalia but has always been called Amalia. I would be surprised if she ends up reigning as Catharina-Amalia instead as Amalia.
The three Danish princes who ended up becoming kings of Greece or Norway changed their names to adopt a name suited for their new country. Wilhelm reigning as George, Carl as Haakon and Alexander as Olav. The last was so young when his name got changed he may not have remembered being called Alexander.
Queen Mary had multiple names but had been known as May of Teck so using Mary was more in keeping with how she was called before her husband succeeded.
Queen Margrethe II is known in the family as Daisy but that is because the French and Dutch version of her name Marguerite and Margriet both also are the name of the flower known in English as a Daisy. Im sure she was called for her grandmother and not for Margrethe I. It just came in handy when it became clear that her parents would not have a son to succeed her father and the constitution was changed to allow female succession.
The Netherlands has it's fifth Queen-consort but Maxima is only the second to use her first baptismal/official name after Anna Pavlovna.
The three others Wilhelmina of Prussia, Sophie of Wurttemberg and Emma of Waldeck-Pyrmont used the name they grew up with but that wasn't their first official name.
I know that in the Orthodox Christianity, a person gets only one name at baptism (exceptions being the children of Crown Prince Pavlos and Crown Princess Marie-Chantal of Greece). So the question of regnal name should never arise, in the event that a person of the faith succeeds to a throne and becomes the sovereign of the country. The man we know in history as Czar Alexander II of Russia, for instance, was baptized as Grand Duke Alexander Nicolyaevich. There was no way he could have chosen (say) Paul or Nicholas as a regnal name later on, after becoming emperor.
But in the world of Catholic and Protestant monarchies, it actually seems to have been a common occurrence for royals to be styled by second, third or even last names, whether or not they succeeded as sovereigns. The woman we know in history as Queen Mary of Great Britain, consort of King George V, was born and baptized as HSH Princess Victoria Mary Augusta Louise Olga Pauline Claudine Agnes of Teck. Her only daughter (who later became the Princess Royal of the kingdom) was baptized as HH Princess Victoria Alexandra Alice Mary of York. Both mother and daughter, however, were known by the name MARY.
Indeed, when you look through the GOTHA, you oftentimes find in italics the names under which the royals were styled -- and the said names would not necessarily have been the first. Has this largely been a matter of personal choice on the part of the said royals, or of their parents? Has there been some kind of underlying principle behind the tradition? I know that even before her husband's accession, Queen Mary was never called Princess Victoria of Teck: rather, she was Princess Mary (nicknamed May, for the month in which she was born). So there never was a question of her being styled as "Queen Victoria" later on, which would have been controversial. But there should have been no problem with calling her Victoria during her maiden days: after all, there were numerous princesses of the realm (and in the continent) thus named.
Indeed, the consort of King Gustaf V of Sweden later on had no problems with styling herself as Queen Victoria. She (born a princess of Baden) had no particular reason to be respectful of the British by using another name, lest she be confused with the venerable queen regnant by the same name. And one presumes that her namesake descendant, the current crown princess, will use Victoria for regnal purposes later on. But Sweden is a different country ...
Is it about respect for somebody else by the same name, fear of confusion over identity (say, mistaking a consort or a non-reigning royal for a sovereign), unsuitability for regnal purposes (the opposite problem: I doubt "Albert" will ever get used as a British king's name, despite some royal men born close in the succession having it as a first name)?
If it came to that, the woman we know in history as Queen Victoria of Great Britain was actually baptized as HRH Princess Alexandrina Victoria of Kent: so even in her case, a name dropping occurred. It all seems to me rather arbitrary ...