Rory is just a nickname for Lorelai. Sometimes shortened versions of names don't always make sense... like Chuck from Charles, Hank from Henry, Peggy from Margaret, Libby from Elizabeth, Dick from Richard, etc etc. That's my assumption at least.
Again it's due to the confusion factor of having 2 lorelai's but I do think that toi can get from Lorelai to Rory... here is my logic: Lorelai can be shortened to Lora ou Lor (like Chris uses in season 7) and Lor is like Ror and everyone always adds a y on the end of nicknames. ou maybe it is just backward logic as not much in the lives of Lorelai and Rory makes complete sence! Hope that toi like my answer
Yes, I think this has crossed every fan's mind. I've thought of it as a chain reaction too. Take Lorelai, shorten it to Lorrie (the plus traditional spelling), then for some reason substitute an "R" in there for the "L" and get "Rorrie" except spelled "Rory". That's my thought process at least.
Gilmore is an Scotch Irish surname, and Rory is a Scoth Irish girls name. With the Gilmore's known tendancy of marrying their own (Grandma Laurelai, aka "Trix", married her cousin) and using family names (3 generations of Laurelai's in the show), it seems possible that Rory is also a family nickname.