It is a rather debated question as both spellings show up in significant publications. The confusion can partly be explained by the actions of the namesake himself: Reinhard Heydrich.

Both at birth and his baptism Heydrich was named Reinhard Tristan Eugen. Therefore, Reinhard, without the t, was his official first name. However, in June 1932 an (erroneous) rumor surfaced suggesting that Bruno Heydrich, Reinhard’s father, was of Jewish descent. It was not the first time that this false rumor circulated. The suspicion stemmed from the fact that the musician Bruno Heydrich was mention in a music catalog as “Bruno Heydrich (eig: Süss)”. Süss being a Jewish name.

It was an error of the editor and it was rectified in the very next print of the catalog. The name Süss belonged to Bruno’s mother’s second husband and he was not his father (nor a Jew, for that matter). The matter resulted in an investigation done in 1932  by the genealogist Achim Gercke, who was in charge of the Nazi Information Office, to establish Heydrich’s ancestry. He concluded that Heydrich was of pure Arian descent. In the Gercke rapport, Reinhardt was written with a dt, as Heydrich himself had started to do himself in those days. He probably thought he would come across more Arian that way.

Later on, Heydrich probably tried to change his name back to Reinhard. This can be derived from the fact that he, on different occasions, tried to change his name from  “Heydrich Reinhardt, SS-Obergruppenfuhrer”, on the annual reports of the important SS dignitaries, back to Reinhard. To no avail.

After the death of Heydrich in June 1942 his extermination program was probably quickly known among the SS as Einsatz Reinhard. A few official documents mention this operation in the actual writing. But these documents don’t clear up the confusion surrounding the correct spelling of his name. In a letter dated November 30, 1943, Himmler wrote to Globocnik confirming the end of Aktion Reinhardt. However, Globocnik himself sent a telegram to Himmler’s warrant-officer Grothmann on September 4, 1942, three months after Heydrich’s death, in which he mentions Einsatz Reinhard. Finally, Herman Höfle, Globocnik’s deputy, for some reason spelled the name, Reinhart.

So, it is not surprising that you still will find both versions, Reinhardt and Reinhard. A majority of publicists who wrote about this subject use the spelling Reinhard but many, among whom Jules Schelvis, prefer the spelling Reinhardt.

The Sobibor Foundation prefers Reinhard, without the t. Not only because it is the most commonly used version and, on top of that, the official name of Heydrich, but also because the alternative spelling has led to confusion in the past: there was speculation that Aktion Reinhard was not named after the conceiver and organizer of the “ Endlösung” (final solution) but after the German minister of finance Fritz Reinhardt, who’s department administered the properties stolen from the Jews that were killed. A program stemming from 1933, which was meant to boost the economy through tax reductions and investments in infrastructure, was named after him: Reinhardt Program.