Each panel will have an 8’ ground rod, check with electrician for code.If the sub panel is located in the same building as the main service panel a ground rod is not required for the sub panel. Yes per the NEC a driven ground rod can be connected to the equipment ground bar in the sub panel. (2017 NEC 250.54) I would not recommend it though.
If the sub panel is located in another building, such as a detached garage, then a new grounding electrode is required and bonded to the equipment ground bar/ panel enclosure/feeder equipment grounding conductor. (Feeder neutral conductor is never bonded to ground in a sub panel. Neutral conductor/ bar shall be isolated from ground/ panel enclosure.)
Minimum required number of driven ground rods for the main service panel technically is one, * IF *, the ground rod to soil resistance is 25 ohms or less.
How can the electrician know for sure if it is 25 ohms or less? With testing equipment that is made to test it. If an electrical inspector sees only one ground he will ask to see a print out of the test. It is cheaper by far for the electrician to just drive two ground rods and be done with it.