There's been some discussion on the matter. In "Mike" he says that Mike can call him Rupert if he wishes, though Psmith would prefer he didn't, so I took that to mean that his name was Rupert and referenced him as such in my fics.

Then, later, in the book where he works for Lord Emsworth (? - I haven't read it, yet) he apparently seems to be named Ronald, and I think he's referenced as such on Wikipedia. (*looks it up*) Yup - Ronald Eustace Psmith, according to Wikipedia (http://en.wikipedia.org/wiki/Psmith). I added the paragraph In his first appearance (in Mike or Mike and Psmith, depending which edition you have) he inexplicably implies to Mike that his first name is Rupert (Although Psmith, being the man that he is, could have done this on a mere whim). (And since I added that, someone else has related an amusing Psmithish incident as an example of selfishness, or perhaps Socialism - *chortles*).

My guess is because the Lord's secretary who he'd just replaced had been named Rupert and Wodehouse wanted to avoid confusion.