What dictates cathode vs anode nomenclature use?
Who was responsible for this naming system and how can we change it?


Michael Faraday was responsible for the terms anode and cathode more than hundred years ago.

All the confusion regarding the nomenclature will vanish if you do not associate electrostatic signs with these two terms. One should identify the electrode labels with the redox processes rather than the signs. 


Cathode: The electrode where reduction occurs
Anode: The electrode where oxidation occurs


These definitions are true whether you have a electrolytic or galvanic cell. This eliminates the need to call the negatively charged electrode as a cathode in an electrolytic cell or the positively charged electrode as the cathode in the galvanic cell. These definitions are self-consistent and hence nobody bothered to changed them.

Isoelectric focusing is "sort" of an an electrolytic "cell" hence its cathode is has a electrostatic negative sign because if we were to remove this gel and replace it with just salt water, we will see hydrogen evolution (= reduction of water) at this electrode.