It could still be that Rabbi Moshe Yirmiyahu Gershon Hakohen Rappaport, Rosh Metivta in Vienna is the same person as Moses Cohen Rapa The main name of Moshe still exists. Could be the other two names didn't get add for some reason. Or the other names were there to distinguish him from other Moshe Rapa's?
Did Wachstein have access to every single tombstone in Vienna? Were all of them around back then? Or did some not survive? I would have expected many many more Rapaport tombstones to have been found there.
I know that there are two different accounts as to who R' Gershon HaKohen Rappaport, Z'L father was. On Geni (According to Wachstein) it was Moshe Rapa. But some hold it was Rabbi Avraham HaKohen Rapa, of Porto. There happens to be a book with Gershon's father as Avraham and not Moshe - as seen here - https://www.kedem-auctions.com/en/content/ramban-torah-%E2%80%93-si...
I was told that the Rapaport family was huge and had lots and lots of descendants and all of therir names were all Simchas and Gershons and Avrahams and Moshes and it was very hard to figure which one was the son of which.
It's very hard to document these genealogies since not so much documentation to prove these relationships.