They were almost certainly aware, but that doesn't necessarily mean that they cared or thought it worth talking about.

The arrival of the English in the British Isles is a key narrative in Bede's Historia Ecclesiastica, which despite being some ~250 years old would still have been a current text in the late 9th and early 10th centuries [MS O (Oxford Bodleian Library MS. Hatton 43) is dated to the 11th Century and MSs. M and N are both dated to the late 9th] and was also one of the predecessor texts which informed early sections of the Anglo-Saxon Chronicle. So the English (or at least the literate English who read their histories) would have known who they were and where they came from. In 930, Æthelstan also celebrated the marriage of his sister to Otto I of 'the Old Saxons', future King of Germany and later Holy Roman Emperor.

This is no real indication that they necessarily cared however, beyond political expediency. Henry the Fowler, King of Saxony, purportedly wanted to ally 'the two Saxon kingdoms' but in the 930s, both the new 'England' and Saxony were kingdoms in the ascendancy with ambitious rulers seeking to secure beneficial alliances, and Eadgyth's marriage to Otto was based most likely on contemporary political realities far more than on centuries-old ties of kinship. Certainly, chroniclers in England took no great interest in affairs across the channel beyond very major events, or really at any point recorded any interest in Saxony or the Old Saxons.