Ludwig van Beethoven was born in Bonn in the Archbishopric/Electorate of Cologne (one of the many German states that existed prior to unification in 1871), like his father Johann. Ludwig's grandfather and namesake was born in the Spanish Netherlands, now known as Belgium. Beethoven's grandfather was a musician of some talent and like many musicians of this era traveled around various princely courts to ply their trade. Eventually the senior Ludwig established himself in Bonn and became the Kapellmeister of the Prince-Archbishop. His son Johann, born in Bonn in 1739/40, followed his father's trade in music as did his illustrious grandson.

The name "Beethoven" is not really a reference to a specific geographic location. In Flemish, the name could mean "beet garden," which was a common name for farmers. The name was also common for tradesmen and merchants, and Ludwig senior's father was a baker who successfully transitioned into selling luxury goods. There is also a subdivision of the Belgian town Tongeren called Betho, so it's also possible that the family name stems from this. Unfortunately, the Beethoven family tree is obscure beyond his great-grandfather, so there is no clear answer.