The only place I can remember where the fans chanted Cristiano's name to Messi was in Portugal, but that's self-explanatory.
The peruvian fans directed ronaldo chants at Messi when ARG travelled there for the WC Qlfs in 2012. I also remember he was greeted with the same at the Ballon d'or ceremony in Zurich.
Obviously, it happens more with Cr, because he's a more dislikeable diva-like figure who's easily baited.