Or Flemish, or whatever they call it. Belgian.
Dutch is the English name for the language of the country we call Holland or the Netherlands. "Dutch" is actually the same word as
deutsch, the German word for "German." It's from the proto-Germanic word (3000 years ago)
thiudisk, "of the people," from
thiuda, "people."
Many Stone Age tribes called themselves "the people" and that name in their language was used by speakers of other languages to refer to them.
Aleman, allemand, etc., the name for Germans in various Romance languages, is from
alle mann, literally "all people" in the language of one of the many German tribes.
Tedesco, the Italian name for them, is from
thiudisk. "German" is from a Latin word meaning "blood relative" and we're not quite sure why the Romans called the Germans that.
The people of Flanders, one of the two major regions in Belgium, call themselves and their language Flemish. However, it is just a dialect of Dutch. Two people from Flanders and Holland understand each other about as easily as two people from Birmingham England and Birmingham Alabama.
The other half of Belgium is Wallonia, the people are called Walloons, and they speak French. The Walloons dominate Belgium politically, culturally and economically, resulting in a backlash of moderate proportions from the Flemish population who feel marginalized. They insist on not calling their language Dutch because they feel that to have their own separate language enhances their claim for independence from Belgium, or at least for more power within a united Belgium.
The Dutch call their country
Nederland and their language
Hollands. The Dutch word
duits means "German."
The unification of a people of French origin and a people of Germanic origin in a single nation, Belgium, is just an accident of history. As European history goes it's not even the biggest accident.

"Belgian" refers to the country's cooking, currency, etc. But not to its language because there are two of them.
The Flemish people would very much resent you calling their language "Belgian" so be careful not to do that! They don't even want you to call it "Dutch." To them it's "Flemish."