Cortinarius betuletorum M.M. Moser ex M.M. Moser, in Gams, Kl. Krypt.-Fl., Edn 3 (Stuttgart) 2b/2: 278 (1967)
Agaricus raphanoides Pers., Syn. meth. fung. (Göttingen) 2: 324 (1801)
Cortinarius raphanoides (Pers.) Fr., Epicr. syst. mycol. (Upsaliae): 290 (1838) [1836-1838]
Dermocybe raphanoides (Pers.) Wünsche, Die Pilze: 125 (1877)
Hydrocybe betuletorum M.M. Moser, Beih. Sydowia 1: 234 (1957) 1956
but why does SpeciesFungorum deprecate C. raphanoides when it’s the older and legitimate name?
C. betuletorum is also described as a form without raphanoid smell and smaller spores, so they are probably not the same species anyway..
MycoBank does not put them in synonymy. Index Fungorum gives priority to Cortinarius betuletorum which was my reference.
C. raphanoides ought to be the preferred name.