How did chlorine get its name and symbol?
The symbol for Chlorine is simply Cl which is just derived directly from its name. The name originates from the Greek word khloros, meaning pale green.
What symbol would represent a chlorine ion that has ionized to have a stable electron configuration?
Sometimes the symbol comes from two consecutive letters in the element name, as with Calcium (Ca), sometimes two non-consectutive letters, as with Chlorine (Cl), or Rubidium. Sometimes the symbol comes from the element's Latin name, like Lead (Pb). Also, two uppercase letters are NEVER used in an element symbol, so Rubidium's real symbol is Rb, not RB.