If I had to use a Lisp-like language, I'd choose Clojure so I can interoperate with the JVM. (I use Scala already, so I could interoperate with that, too.)
Suppose that we have used (cddr x) to test whether the list x continues after the second item. It is then unnatural to have (third x) to retrieve the third item! It is like "faulty parallelism" in your English essay. :)
If the condition (and (cdr x) (consp (cddr x))) holds, then the proper way to get that item is (caddr x). This is easy to verify: If cddr is a cons, then its car is given by tacking on an "a": caddr.
In any case, car, cdr and the rest are an absolute must in a Lisp dialect. They are instantly understandable; there is no good reason to break with this important convention. A Lisp dialect will not achieve anything by breaking cultural compatibility with other dialects in this regard; it will just be shunned by Lisp people yet still disused by everyone else. Although CAR and CDR come from IBM 704 machine language, which means nothing to pretty much anyone over fifty years later, the people who allowed these names to infect the higher level language weren't idiots. They discovered that the names just work and so used them. Borrowing some mnemonic that works from the IBM 704 is no worse than borrowing some equally arbitrary greek letter like lambda from a branch of mathematics. If the mathematics of anonymous functions had been called "Tau Calculus" we would be writing (tau (x y) + x y) instead of lambda; it's just a historic accident. All names are historic accidents: one person calls it water, another one aqua, a third one mizu.
I also love the star convention and have used it in many places. for instance mapcar* is a lazy mapcar: it can take infinite lists as its arguments and returns the resulting lazy list immediately. Leslie Lamport picked up on this star notation in LaTeX; that's where I first encountered it. When I got into Lisp years later it was like, hello, is that where Lamport got it from?
I don't like verbosity, so I made my dialect slick and ergonomic. It can "code-golf" side by side with the so-called "modern" scripting languages, while remaining clear.