Rothbard's family name

Something occured to me. Seeing that Rothbard’s ethnic heritage was Askenazi how would his surname be pronounced originally, while they were still in the old country?

I am not sure but I think there is no ‘th’ (soft t) sound in German. So, would it be pronounced with a ‘t’ sound and an ‘h’ sound or would the ‘h’ be silent, or what?

I’ve always pronounced it wrou (as in wrou-ght iron fence) th (as in theology) bard (as in the historical term for a pre-industrial entertainer).

AKA - exaclty how it looks haha