The name of the station comes from the junction named Croix-Rouge, situated at the north-eastern end of the Rue du Cherche-Midi. The name had previously been in existence for several centuries. It is unrelated to the International Red Cross and Red Crescent Movement (generally referred to in French as the Croix-Rouge), founded in 1863.
The bus stop at the same location retained the Croix-Rouge name until 31 December 2005, when it was renamed Michel-Debré, after Michel Debré, first Prime Minister under the Fifth Republic and co-author of the Constitution of France. Apart from the street sign Carrefour de la Croix-Rouge at the junction, there is therefore no longer any official trace of the name.