This is a very good question, Z.
I have looked at a lot of Ric Ocasek / Richard Otcasek sites for a definitive answer. I am close, but no quite there yet.
So far the best I can do is shed some light on the context for the name change. The history of the pre-Cars era for the two primary musicians records, "Otcasek and Orzechowski would remain together. Inspired by proto-punk outfits the Modern Lovers, the Velvet Underground, and Roxy Music, they formed Rick & the Rabbits and changed their last names from Orzechowski to Orr, and Otcasek to Ocasek".
Also, "After Milkwood, Ric and Ben put together another group called Richard and the Rabbits, whose name was suggested by Jonathan Richman. They were a local club band for a while. Soon after, Greg temporarily left Ric and Ben and joined up with groups including Orphan, a soft-rock band, and Martin Mull and His Fabulous Furniture, who worked in musical comedy, where he played a variety of instruments. Ric and Ben then performed as an acoustic duo called Ocasek and Orr at the Idler coffeehouse in Cambridge."
Interesting history, but not quite the answer to your question, Z.
https://www.dispatch.com/article/20090405/NEWS/304059564