Anodes are always +ve in an externally driven electrochemical process (like plating, corrosion removal, or battery charging).
Strictly speaking yes the oxidation and reduction reactions determine the electrode name and yes that can change the polarity in a battery-type reaction depending on whether it is being charged or discharged. I see now what you mean by your 'what you are doing'... comment
FWIW there is a third very common circumstance, in corrosion (which is like the galvanic cell above, only without an external load in the circuit); the anode and cathode are at the same potential (they are often different locations on or parts of the same object) and the potential difference that drives the current could be said to exist in the electrolyte/surface material on the electrodes.
cheers