Clitocybe nuda is a widely used synonym. According to Index Fungorum both names are currently (June 2007) valid, so I’m leaving it that way for now.
The issue here revolves around an on going debate about the correct type for the genus Clitocybe. Some, including Singer and apparently the folks running Index Fungorum, take the type to be C. gibba. However, the growing opinion (and I believe at this point the majority of experts) takes C. nebularis to be the type. If you take C. nebularis to be the type then Lepista is becomes a deprecated synonym of Clitocybe and Clitocybe nuda is the correct name.
This species is also very similar to Clitocybe glaucocana. According to Denise Gregory’s key to Clitocybe in California, they can be distinguished based on the cap color when young. In the case of C. nuda they should be deep violet or purple. C. glaucocana, on the other hand, is light violaceous, light blue or faintly purple when young. It would be nice to know if there are other reliable ways to distinguish between the two species.