As far as I can tell, the name "Rothschild" originated from the house where the famous Maier Amschel Rothschild lived in the Frakfurt Jewish Ghetto, 'zum roten Schild' (at the sign of the red shield).
The Kingdom of Prussia began sequentially requiring Jews in its eastern provinces to adopt surnames in the 1790s, an edict affirmed by Napoleon Bonaparte following his invasion of Prussia in 1812. Surnames were derived from a variety of sources, such as the personal names of ancestors, place names, and occupations (Source: Wikipedia).
SInce Maier Amschel Rothschild was born in Frankfurt (in the Holy Roman Empire) in 1744, and our ancester Maier "Rothschild" was born in Baierthal (Baden) in 1755, it would appear there could be no relation between the two, and most likely our ancestor Maier in Baierthal adopted the surname Rothschild sometime in the time period 1790 - 1812 to conform with the edict.
