Taken from E. Mullins' masterpiece - Secrets of the Federal Reserve:

The sire of the family, Mayer Amschel Rothschild, established a small business as a coin dealer in Frankfurt in 1743. Although previously known as Bauer*, he advertised his profession by putting up a sign depicting an eagle on a red shield, an adaptation of the coat of arms of the City of Frankfurt, to which he added five golden arrows extending from the talons, signifying his five sons. Because of this sign, he took the name ‘Rothschild" or "Red Shield".

Taken from E. Mullins' masterpiece - Secrets of the Federal Reserve:

The cover reproduces the outline of the eagle from the red shield, the coat of arms of the city of Frankfurt, Germany, adapted by Mayer Amschel Bauer (1744-1812) who changed his name from Bauer to Rothschild ("Red Shield"). Rothschild added five golden arrows held in the eagle’s talons, signifying his five sons who operated the five banking houses of the international House of Rothschild: Frankfurt, London, Paris, Vienna, and Naples.