The best in my opinion is to get this kind of insurance while still in Germany and keep it in when you are in the US - just check that the insurance you purchase is valid worldwide without temporal limitation, even if you move abroad.
I checked before moving to the states, and there is nothing comparable to a Haftpflichtversicherung in the German sense (the US insurances are more expensive, don't cover some risks and/or cover other thinks that I don't consider to be worthy to insure).
I chose the Interrisk XXL Haftplicht (see below), but there are probably other providers that also offer worldwide coverage.
I am not a lawyer, but I based my choice on how they define their coverage in foreign countries ("Bedingungen zur Privathaftpflichtversicherung XXL / Verbindliche Erläuterungen zu den B68 / Zu § 1 Versichertes Risiko"):
"Versichert sind sämtliche Risiken des täglichen Lebens als Privatperson, also beispielsweise [...] während Auslandsaufenthalten ohne zeitliche Begrenzung"
Maybe my interpretation of this definition is wrong, so you should consult with the insurance company, or with a lawyer.