In the German Encyclopedia of Names by Hans Bahlow the place name Weppel/Münster is explained as deriving from Wepel  = swamp. That means that there was a farmer living near a bog or swamp, whose farm was named „der Wepel„  It indicates a location – a feature of nature.  Thus the name is most likely derived from a location.  Family names derived from the place of residence are an older form of creating a name in the German language.  With an increase of the population during the Middle Ages, people began to use professions as "house names" such as Zum Schmied (Smith), Zum Wagner (Wagoner), etc. It could very well be that our name has been in use for more than a thousand years. 
In  Oelde   the name „Wepeler„ is first documented in 1250.  Later on the name evolves into „ter Wepel„, „Zum Weppel„, „Schulze Weppel„, and from the 16th century onward into Weppelman(n), subject to a variation of spellings. 
The name „Wepeling„ or „Wepelinch„ from Ottmarsbocholt/Ascheberg is a patronymic, for example Hans Lamberting = Hans, son of Lambert, Volkmaring = son of Volkmar, or Everdynk = developing into Evermann. 

Wepeling is certainly a later form: son of Wepel, the holder of a farm named „Wepel„. „ Weppel„, later  „Weppelman„. All the different forms are in use well into the 16th and 17th centuries.
Following the theory that the name „Wepel„ is derived from a location, it is possible that this name came into use at the same time in different localities. The usage of the name must therefore have been accomplished between 1000 and 1200.  The name Weppelmann is attested to in 1484 by a witness Bernard Weppelman, who appears before the court in Ascheberg. But even the name "Weppel" remains in use:  During my research I discovered Anna Gertrud S. Weppel, born in Beckum, Westphalia, in 1801.  Even today there are about 10 „Weppel„ listings in the telephone directory. Whether they belong to our family still has to be researched. That errors in spelling occurred repeatedly is clearly shown in the names of Anna Katharina Webbelmann, who was born in Ibbenbüren, Westphalia, in 1812, but used the variant „Weppleman„ in the USA. 
From about 1840 on, Weppelman is usually spelled as Weppelmann. This was the result of a spelling reform, only fully implemented in 1880. 

Therefore I have spelled all the German „Weppelmann`s„ with a double „n„, and I have retained the original form Weppelman for those in the Netherlands, America or South Africa. 
Our origin is very likely the „Schulzenhof zur Weppel„ in Ahmenhorst Nr. 27, providing us with the oldest available records.  (A „Schulte" is a farmer who was financially in a position to sublet land) 
The present owner is Antonius Schulze-Weppel, Letter Straße 25, born on Nov. 14, 1956. 
* According to the oldest information, taken from the „Westfälischen Urkundenbuch„ by Willmanns, the old Schultenhof was leasehold, granted to the family de Wepele by the Monastery Freckenhorst. 

Note:  The farm was probably called Wepel, but the farmer/tenant living there could have been called "der Wepel". The "der" can be seen as the German article as in "der Wepel-Bauer", or "der Wepel", it could also have been used similar to the Dutch, as in "ter Wepel" = the ones living at Wepel.