What is The correct terminology for expressing *this* notion of complexity
Kolmogorov's complexity is defined relative to a specific representation. It is rather meaningless to ask what is the minimal Kolmogorov complexity of a certain object over all possible representations (obviously, this requires a precise definition for what constitutes a valid representation).

To see why, consider for example the following question: what is the minimal Kolmogorov complexity of the identity function over all admissible numberings? The answer is trivially $1$, since I can encode the identity function as "0" (a single bit string).