The first member of the family who was known to use the name "Rothschild" was Izaak Elchanan Rothschild, born in 1577. The name is derived from the German zum rothen Schild (with the old spelling "th"), meaning "with the red sign", in reference to the house where the family lived for many generations. (At the time, houses were designated by signs with different symbols or colours, not numbers.)
I wonder why they're called "Red Shield" (translated from German)
https://infogalactic.com/info/Rothschild_family