I believe the name comes from the Bega River in Germany. It is located in the Lippe Province in the Rhine Valley. 5 towns in particular, Bega, Bosingfeld, Barntrup, Detmold, Schoetmar, and Wuesten. Another very large branch settled in Groningen NL. originated in Oldenburg Germany.
June Begeman and others have provided us with a copy of the family crest (or coat of arms or large drawing), it depicts a man with a knapsack and back pack walking along a river. High above him is a castle from which a flag is waving. On the other side of the river can be seen a church. It dates back to 1817. (There are others but the man on the river is the most predominant.) Although it is associated with the Begemann name, I believe we are one in the same.Steve Begeman wrote in with some wonderful insight
I also believe that the name Begemann means "Man from the river Bega". The Bega river is located in the Lippe Province, but the Lippe Province is NOT part of the Rhine Valley. The Lippe Province is similar to the territory formerly known as the Principality of Lippe until 1945. After World War II it was part of the British Occupied Zone and later it was included into the newly formed state of Northrhine-Westfalia. The Lippe Province is part of the sub-region East-Westfalia/Lippe. As you can tell by the name, the Lippe province is located between the eastern part of Westfalia and the state of Lower Saxony and is not a part of the Rhine Valley. There are also no vineyards in the Lippe Province.
You mentioned the different spellings of our family name (with one n or with two n). I always believed that the people who emigrated to the US dropped one n because a double n is unusual in the English Language. You can also see that at other names as Bergman, Zimmerman etc.. Because MANN (german) means MAN (English), I always thought that they just dropped the letter so it was easier for the non-German citizens to spell the name. But that's my theory. There is no difference in the German and Dutch spelling of the name. Both sides write it with NN. Also, I don't think there is a difference between a Christian and a Jewish spelling or a difference between North and South Germany.