Peter Eichfuß (of the Statistical Bureau of Baden-Württemberg) supplied the following historical and linguistic search results: In principle we are dealing with two parts of the name: pan (bann) and holz. Little explanation is needed to determine that -holz stood for today's word of -wald (Engl.: forest). Other forms found in combination with ban(n)- include -forst, -horst, -hag. Woodland districts, having never been disposed of in the first distribution of lands, were often held to belong to the king who, by way of a special law, a "ban", set them apart for his pleasure hunting, and installed wardens (bannwart) for the purpose of guarding and maintaining them. The King could transfer this right (ban) to feudal lords, particularly Counts. (Emperor Friedrich II transferred this right to the souvereigns of the German principalities, who extended it to include their entire territory!!!).
Roots for the word ban can be found in Latin legal texts bannus, bannum edictum, interdictum, proscriptio, in Old-High-German pan, pannes, in Middle High German ban, bannes ( in Frisian bon, in Danish band, in French ban, bannir). Ban signified the authority and jurisdiction exercised by the ecclesiastical or feudal ruler (bannherr, Latin: aedilis curulis). But ban also designates the district covered by such power of the feudal lord (bannherr), such as Bannmeile (a circle with the radius of one mile around a town, serving as Markt- und Zunftrecht proclaimed legal district no foreigner could exercise any profession or trade. Linguistic links of this survive in the French word banlieue, or suburb, and - possibly - in the German word Band, ribbon). After the Dark Ages, during Christianization, the sacred inviolable forests of pagan times were often turned into hunting forest reserves for the king (bannholz, bannforst, Latin: lucus). "ein bannholz finster und weit" FRONTIN bei Facius 1,11,10. FRONSP. 3,240*; bannholz der abgöttin Diana.