According to the French Wikipedia article, in 1952, after a visit in Hamburg, Collatz explained the problem to Helmut Hasse, who brought the problem to the US i

According to the French Wikipedia article, in 1952, after a visit in Hamburg, Collatz explained the problem to Helmut Hasse, who brought the problem to the US in the university of Syracuse, hence the name "Syracuse problem". So this name appears after the 2nd World War, at a time when the relations between France and Germany are becoming friendlier (https://en.wikipedia.org/wiki/France%E2%80%93Germany_relations#France.2C_Germany.2C_and_United_Europe https://en.wikipedia.org/wiki/France%E2%80%93Germany_relatio...). I guess that French researchers heard about the problem from someone from the university of Syracuse.