As far back as recorded history, Swedes, Danes and Norwegians are all separate people. The Sagas and Eddas and so on all refer to them seperately, as do Viking Age runestones and such. In fact there are more nationalities; present-day Swedes was not a concept in the Viking Age; they consistd of Svear (in Swedish, Svíar in Old Norse, pro-Germanic *swihô) or "Swedes-proper" as well as götar (Old Norse gautar and not least Old English geatas), as well as the Gutar, the inhabitants of Gotland. The latter two names likely have the same etymological origins. Some present-day Danes would also have been Frisians. These are the groupings that meet us in the earliest substantial literature, from the Viking Age. However they go at least twice as far back;

Around the year 100, the Roman historian Tacitus wrote of the north Germanic suiones and gotones, usually associated with Svear and Götar, which would be the In the second century Ptolemais also writes about Γαυτοί (gautoi) in the area.

At some point we also have the Goths who (if Jordanes is to be believed) emigrated from south Sweden. Around the 1st century to the the Gdańsk Bay on the Baltic coast the Wielbark culture arises, which is associated with the Goths But we cannot say this confirms a migration though; cultural contacts are evident from archaeological finds, so in any case it's likely that the Goths also had at least a common name origin Götar, as another testament to how old the name is. (From the Renaissance to the 19th century, they would be considered to be the same in nationalist Swedish historiography, and what you would consider 'Norse' today would've been referred to as 'Gothic' by Swedes then, such as Olaus Magnus description of runes as Alphabetum Gothicum)

By around the 9th century, Beowulf is written down, and it too has these Svear and Götar and Danes and so on; Beowulf himself is a Geat (Göt), who goes off to help the Danes. Further subdivisons are there that would continue later as well; the Götar are divided into east and west Götaland, Danes are divided into Danes and Jutes and there are also specific groups of Danes with fanciful names like the Spear-Danes, Bright-Danes and Ring-Danes. The story is also testament to close cultural contacts here, and also with the Angles and Saxons, who preserved the story.

Close contacts does not make for a single cultural identity though. Although there was a certain identification for Scandinavians as a whole and the common language as 'northern' (norrœnn). However the term norrœnn when used for a specific person/ethnicity meant Norwegians. Which should not be interpreted a Norwegian common identity though. Just as there are many separate terms of 'north' origins in the modern languages. Just as in English 'nordic', 'norwegian' and 'northern' are separate.

In Swedish from norr (north) there's nordisk (nordic), nordbo (Nordic person, 'inhabitant of the north'), norrman ('northman', Norwegian person), Norge, ('north way', Norway), norsk ('northish', Norwegian thing), norsk (Norwegian person, slightly derogatory), norrbagge (Norwegian, even more derogatory), norrländsk ('northlandish', a person from north Sweden), nordländare ('northlander', a person from Nordland in Norway), fornnordisk ('ancient nordic', Old Norse), norrön ('of the north', Old Norse, somewhat rare).

What the language does not have though, is a term corresponding to 'Norsemen' or 'the Norse' no collective grouping of Scandinavians specific to the Viking Age or any other period. Because the collective terms they used were essentially the same used up to present day, and there was no particular need to single out a particular time period. For the Englishmen on the other hand, it makes sense since they were being raided in that period and by people from across Scandinavia. So the term both derives from and perpetuates the Anglo-Saxon view. Which is not to say it's a bad term; in many contexts it's entirely sensible to use it, but it is an outsider term and there's not much reason to think it ever existed as a common identity. On the contrary the evidence suggests there were more cultures and identities.

To take yet another example: the Finnic word for Sweden is Ruotsi/Rootsi, comes from referring to Roden area of Uppland in Svealand in Sweden; i.e. the coastal area nearest Finland. Even though the term 'Svear' or its antecedents probably existed at that time, this may have reflected that the local Rosbyggiar identity was perhaps stronger than their Svea one, also seen with the Rus' being remembered as Rus', if we accept the common idea of Rus' origins in Roslagen.

(of course 'Finn' is itself a collective outsider term by Scandinavians used for all Finnic peoples who were considering themselves to be Tavastians,Savonians, Karelians, etc in that era)