tabs: [{
    name: "Step 1",
    DroppedDetails: [
      { name: "Bhanu" },
      { name: "Sagar" }
    ]
  },
  {
    name: "Step 2",
    DroppedDetails: [name: "Bhanu Sagar"]
  }
],

{
  name: "sagar111"
}

tabs: [{
        name: "Step 1",
        DroppedDetails: [
          { name: "Bhanu" },
          { name: "Sagar111" }
        ]
      },
      {
        name: "Step 2",
        DroppedDetails: [name: "Bhanu Sagar"]
      }
    ],

const { tabs } = this.state;

// here you code to decide what tab do you want to update
const tabSelected = tabs[0];
const { DroppedDetails } = tabSelected;
DroppedDetails[0]= {
  name: "sagar111"
};
// You can edit another one or add a new one to the array also.
DroppedDetails[1]= {
      name: "NameEdited"
    };
DroppedDetails.push({ name: "New Name" })

this.setState(
{ tabs: tabs.map(t => t === tabSelected ? { ...tabSelected, DroppedDetails }) : t });

this.setState(tabs);

const { tabs } = this.state;

tabs.map(tab => {
  // Do something with your tab value like the following
  const newDroppedDetails = tab.map(({ name }) => ({ name: name.toLowerCase() });
  return {
    ...tab,
    DroppedDetails: newDroppedDetails
  }
});