I think writersoul is correct about hakaras hatov. An example that comes to mind would be that after the whole incident with Alexander and Shimon Hatzadik (Yoma 69a) the Jews named their kids Alexander (as recorded by Josephus). Now perhaps one can argue that that was not because of hakaras hatov inasmuch as it was to gain favor with Alexander. But R’ Moshe assumes that it was hakaras hatov and that in fact that would be a proper manifestation of hakaras hatov.
Igros Moshe O.C. 5:10:
??? ?????? ???? ????? ??? ?”? ????? ???????? ???”? ????? ?? ??????? ??? ?????? ???? ???? ???? ?????? ?? ??? ??? ?? ??? ??? ???? ???? ????? ???? ????? ?? ???? ??? ???? ???? ????? ?? ????? ???? ?????? ??? ?? ?????
Interestingly, it seems that it was appropriate to do something which was a ???? as a display of hakaras hatov, so surely simply acknowledging a favor from someone (even of a different religion) would be ok.