The Netherlands has, in a way, always been an individual region. You might not refer to them as Dutch though because that would connote a person from the whole Germanic region. Diet was the earliest way they referred to themselves, but that is in Dutch. Most likely you would say it is someone from the low lands or Netherlander. Since English speakers had the most contact with the "Dutch" people, the term shifted to someone from the Netherlands, but this is not until later in history, and after the Middle Ages. Despite this, someone could refer to them by their specific region, for example you might say Flemish or Frisian.
I've always wondered this, too. How did "Dutch" come to be associated with the Netherlands? "Dutch" must originate with "Deutsch" which is clearly German, but Netherlands just means low lands and Holland is only one region within the Netherlands. Where does Dutch fit in? I've asked every Dutch person I've met and none of them knew.
There were multiple written languages in late medieval Germany. The Hanse had it's Hansedeutsch; the Catholics had Jesuitendeutsch. It was abolished by Maria Theresia in 1774 because all the most popular books were only avaible in Lutherdeutsch. She didn't want her state to speak a language that no educated person understood.
In the Middle ages what is now The Netherlands didn't exist as a specific cultural and political entity. The low countries were divided up in different duchies, which were distinct political entities, ruled by their dukes. You still find traces of those dutchies in the names of the provices in both Belgium and the Netherlands. E.g. Noord Brabant (NL) and Vlaams/Waloon Brabant (BE), Oost and West Vlaanderen (BE) and Zeeuws Vlaanderen (NL) and both countries have a provice called Limburg.
Those Dukes would be allegiant to the French King, others to the Emperor of the Holy Roman empire. Sometimes switching between them.
But the people living in those parts would have considered themself to be Limburigans, Frissians, Hollanders, Flemmings or Brabantians.