The name originally given to element 61 by the group whose 1945 discovery was accepted by the international authority the
IUPAC, who however in 1949 changed the spelling to the modern
promethium. It was named after the titan
Prometheus who in Greek mythology brought fire to humans. Earlier claims for discovery of element 61, given the names
florentium,
illinium, and
cyclonium, were all rejected.
The existence of the element between neodymium and samarium was predicted in 1902 by Bohuslav Brauner. (It was not until quantum theory in the 1920s that the atomic number concept could be used with confidence to say that, there being elements 60 and 62, there must be an unknown element between them.) Searches for it in the next decades had some success but it was the 1945 claim of Jack Marinsky, Lawrence Glendenin, Harold Richter, and Charles Coryell at the Clinton National Laboratory (now Oak Ridge) that was accepted. Grace Coryell (Charles's wife, I suppose?) proposed the name prometheum.
http://homepage.mac.com/dtrapp/Elements/myth.html#Pm
http://vishnu.glg.nau.edu/people/jhw/PmClub.html