As another (good) answer went into, the Etymology of "England" goes back to the Germanic invasions that happened during the time of Badon Hill (the historical setting for the initial tales of King Arthur, roughly 500AD).
There was a recorded sermon discussing the recent history of the island written not long after then, that mentions the battle: Gildas' De Excidio et Conquestu Britanniae. That roughly translates from Latin as "The Ruin and Conquest of Britain. So our documented evidence is that locals of letters at the time referred to their island as Britain.
Another popular previous name was Albion (Ἀλουΐων in Greek), but that name appears to have gone out of fashion sometime after the first century.
Due to its etymology, most likely the term "England" initially only referred to kingdoms (lands) run by Old-English speakers. In a way, this is still the proper usage:, since technically England is a country (separate from Scotland and Wales), the (separate from Scotland and Wales), and the island is Britain.