They did use all three names - they took the "London" from London Scottish, the "Irish" from "London Irish", and "Rugby Club" from Richmond!!!
Actually I believe they were forced by the RFU to merg, and created a company "Irish, Scottish, Richmond Ltd" to run a single team - and although they incorporated a band around the arm with the Richmond and Scottish colours, they were called London Irish.
Richmond's website doesn't even make mention of this - they simply say they went into administration in 1999 and their right to playin the premier division was removed. Say they didn't reform until "Richmond Vikings Ltd" re-financed them in 2002.
I think it was a bit like Hull and Gateshead rugby league teams merging when Hull were in danger of disappearing ... and they called the merged team "Hull" - must have been up all night thinking up that one!!