How can we understand portable battery for mobile phones having 10000 mAh capacity, and 6200 mAh "nameplate capacity"?
Quite simply - they are lying to you, and including the "nameplate capacity" so that they can try to cover themselves.

Batteries are typically rated at 1C discharge - this means at a current level that will discharge the battery to the minimum safe level within 1 hour. So a 10Ah battery will discharge at 10A for 1 hour.  If the nominal voltage was 3.7V, we can ballpark by saying that's 37Wh.

You can get maybe +5% by discharging a battery at a lower current - so for example 2A will probably get you 38.5Wh because there's less loss due to internal resistance (remember higher current = more lost due to resistance).

But you're not going to take a 6Ah battery and turn it into a 10Ah battery by using it differently.

I expect if you take any of these battery packs and run your own tests, you'll see. They rely on people not knowing any better and just buying something because it says that it's higher capacity.