As we often say here, it’s really difficult to answer why something didn’t happen - in this case, the only real answer is “no one has ever bothered to take the regnal name Alfred II”. But of course there is a bit more to it than that.

In fact, since the Norman Conquest, no kings or queens have taken any pre-Conquest names, except the eight Edwards, and until Edward I there weren’t any royal children at all who had Old English names. Here are some of them:

William I - Robert, Richard, William, Henry, Adelaide

Henry I - Robert, Richard, Reginald, Gilbert, Fulk, Matilda

Henry II - William, Henry, Richard, John, Geoffrey, Joan, Eleanor

John - Henry, Richard, Joan, Isabella, Eleanor

Henry III - Edward, Margaret, Beatrice, Edmund, Katherine

Before Henry III, none of them had Old English names. Their stock of names came from continental Germanic names, through Frankish and Latinized through French, except for the occasional Biblical name (John, the feminine form Joan, Katherine).

Henry III broke the trend though:

“The language of the court and nobility was French, yet the baby was given an English name. This was Henry III's personal choice, reflecting his devotion to the cult of Edward the Confessor, who had been canonized in 1161. The feast of the saintly king was always celebrated with great pomp by Henry: in 1263 he hoped to feed no less than 100,000 poor men on the occasion. In 1220 he had laid the foundation stone for a new Lady Chapel in the Confessor's church, Westminster Abbey, and in 1245 he was to begin a full-scale reconstruction of the whole building in the latest French style. The cult was designed to add to the prestige of the monarchy, and to this extent the choice of the name Edward had political implications. Essentially, however, it was the product of Henry's personal piety.” (Prestwich, pg. 4)

Henry also named another son Edmund, after the 9th-century East Anglian king Edmund the Martyr. While Alfred was remembered as an important, wise, and pious king, he was not venerated as a saint, so his name never became part of the pool of names used by the ruling class, at least not in the Middle Ages. There were a couple of modern royal children named Alfred, one a son of George III who died as an infant, and the other, the second son of Victoria, who was Duke of Edinburgh and Duke of Saxe-Coburg-Gotha. Victoria’s son Alfred doesn’t seem to have been named after Alfred the Great, as far as I can tell, but I’m not sure who he was named after.

Alfred’s elder brother, Albert, became king and adopted the regnal name Edward VII - not necessarily because he was honouring the previous Edwards, but simply because it was his middle name, and then here had never been a King Albert. If Albert/Edward had died and Alfred had become king, would he have kept the name Alfred? Would he have used one of his other names (Ernest, Albert)? Or would he have chosen a name that had previously been used, like Edward? Of course we have no way of knowing.

As for the kings named George, it’s possible that the more recent ones were recalling St. George, the patron of England, but in fact all of their given names were George (although George VI’s first name was actually Albert). That name came from the pool of names used by the House of Hanover in Germany. The popularity of the name George probably had something to do with the dragon-fighting saint, but he was a popular saint throughout the medieval Christian world, so the use of the name George by the Hanoverians wasn’t directly related to the adoption of St. George as the patron of England.

So in short, the kings of England/Great Britain/the United Kingdom have never used any pre-Conquest names for their children. The exception was Henry III, who named two of his children after Edward the Confessor and Edmund the Martyr, two saints whose veneration was important in 13th-century England.

Sources:

Michael Prestwich, Edward I (Methuen, 1988)

Michael Prestwich, Plantagenet England, 1225-1360 (Oxford University Press, 2005)

David Carpenter, Henry III (Yale University Press, 2020)