Just wanted to point out that the name of your general doesnt change to "Satrap Glueos Stickos" for example.

And these satrap titles are ancillaries and shouldn't be hard to obtain neither easy. You have a general with low Influence the chances are more slim. There are some set criteria.
However as they are ancillaries, you can swap them around if you want, so if you think that no good Dionysos-loving drunkard of a son who'd probably spend all taxes on a major temple to Dionysos with fountains of wine should be satrap in Media say, feel free to swap