Clojure did not just rename a few functions. It's basically zero source code compatible with Lisps. Not only old example code does not run, nothing runs. No applications, no libraries, no tools, ... It's not even easy to port. It's a rewrite and/or redesign.
Obviously this is okay for people who don't care of the historical baggage (and want to avoid it) and who don't care about the functionality of Lisps, like interactive error handling.
That used to be different. There were Scheme programs running in both Scheme and Common Lisp or moving between them. For example the Yale Haskell compiler was originally developed in a Scheme dialect called T and then moved to Lisp (here Common Lisp) by embedding a shallow compatibility layer in Lisp. Another example is Common Music, a music composition system, which ran for a while both in Scheme and CL. Scheme itself was originally a hosted program on top of Maclisp. A few more Scheme implementations were written and/or embedded in Lisp - for example the Scheme variants for Naughty Dog's Crash Bandicoot and Jak and Daxter Playstation games were written in Common Lisp. The Scheme written by Peter Norvig was used in a content management system, embedded in CL.
Nowadays I don't think of Scheme as a mainline Lisp -> it moved from a close Lisp dialect to its own language with its own standards, books, user groups, libraries, implementations, applications, ...
Right. The reason Common Lisp is called “common” is that it has a standard that allows anyone to build a lisp from scratch that will run any common lisp code essentially completely unchanged (obviously you need to adjust a bit where you hit the OS, but even the file access methods are spec’ed). If you aren’t conformant you aren’t a Common Lisp - you could still be a lisp. Clojure is a lisp, just not a Common Lisp.
Obviously this is okay for people who don't care of the historical baggage (and want to avoid it) and who don't care about the functionality of Lisps, like interactive error handling.