There is, of course, zero evidence that AR was named after FR. Not a single shred of documentary or testimonial evidence seems to exist for this hypothesis.
One might argue that there is no such evidence for AR being named after Heydrich.
However, first of all, we know that Heydrich's name was spelled both "Reinhardt" and "Reinhard".
There is no evidence that FR's surname was ever spelled "Reinhard".
In numerous documents AR is spelled "Aktion Reinhard". That excludes Reinhardt as a sole source of the name outright.
So even if there was no positive evidence for Heydrich as a source of the name, we could arrive at this conlusion by merely excluding FR.
Also, there is a piece of testimonial evidence, namely, SS-Ostubaf Karl Ernst Moeckel's testimony in Polish captivity. Moeckel was Leiter der Abteilung Verwaltung in Auschwitz, and knew in and outs of the "business". In his deposition of 07.07.47 he claims (Bertrand Perz und Thomas Sandkuehler, "Auschwitz und die "Aktion Reinhard" 1942-45. Judenmord und Raubpraxis in neuer Sicht", in: Zeitgeschichte 5, 26. Jg., 1999, S. 303):
All this said, I don't see why it's not possible that, as time went by, "Aktion Reinhardt" became an allusion to both Heydrich and Fritz. This, however, is a mere conjecture, and in any case Heydrich is the "main" source for the name.Bei Aufnahme der Dienstgeschaefte in Auschwitz bestand bei der Haeftlingsgeldverwaltung eine Abteilung: "Verwertung beschlagnahmten juedischen Eigentums aus Aktion "R". Mein Vorgaenger erklaerte heirzu, dass die Aktion "Reinhard" hiesse, nach dem Vornamen des frueheren Chefs der Gestapo Heydrich und angekommene Judentransporte betroffen hatte.
2. There seems to be no evidence linking Chelmno to AR except the report about Paul Blobel building "Feldoefen Aktion Reinhard" there, but the name of these experimental "ovens" doesn't prove that Chelmno itself was part of AR as a killing operation. It is possible, of course, that the belongings of Jews murdered in Chelmno were acquired under AR auspices, but that in itself doesn't make Chelmno an AR camp. Conventionally, AR camp is a camp in which Jews were murdered in the course of AR proper, and, according to the Hoefle telegram, these camps were Belzec, Treblinka, Sobibor and Lublin (Majdanek). If Chelmno was an AR camp, it would probably be included in the telegram.
There is, however, some uncertainty regarding this. It seems that Bunker 2 at Auschwitz was named (at least once) "Station 2 der Aktion Reinhard". While that wouldn't necessarily make Auschwitz into an AR camp, it seems to indicate that AR killings might have been going on in the camps not listed in the Hoefle telegram...