Most experts think that it has to do with the fact that in the seventeenth century the Beethoven family was a family of Catholic farmers, living in Flanders. The word "beet" (these days spelled "biet") means, not surprisingly, "beet". The word "hof" (plural "hoven") means "garden", not only the grounds, but also the buildings. Some researchers point to a part of the Netherlands, called the "Betuwe", where a long time ago a (German?) family had found "better meadows" (the prefix "bet" meaning "better") and later on travelled southwards to Flanders where they settled down. In Flanders there was a locality called Betouwe and in the sixteenth century it's mentioned in the archives as Bethove or Bethoven. Anyway, the use of "van" ("from") does suggests that the name points to a particular place, be it the original "better meadow" or the later one developed "beetgarden". In the sixteenth and seventeenth century the name was also spelled as "Piethoff(en)," "Betthoff(en)," and "Biethof(en)." A third group of experts points to the noble family de Bethues, living in Limburg, the most southern part of the Netherlands. But the most amazing digression is one by a French researcher who saw a connection to the Portugese noble family de Bethos. This family was a family of slave-traders who found their slaves in, of course, Africa. And then the story of Beethoven's black blood comes to mind again. But these days most researchers believe in the not-noble connection to the Catholic farmers and most probably they are right.
Schmidt-Gorg, Joseph. Beethoven. Die Geschichte seiner Familie. (Bonn, 1964).
Schmidt-Gorg, Joseph. Des Backermeister Gottfried Fischer Aufzeichnungen uber Beethovens Jugend. (Bonn, 1971).
Mann, Werner. Beethoven in Bonn. Seine Familie, seine Lehrer und Freunde. (Bonn, omstreeks 1982).
Wetzstein, Margot. Familie Beethoven in Kurfurstlichen Bonn. Neuauflage nach den Aufzeichnungen des Bonner Backermeisters Fischer. (Bonn, 2006).