Like this

// Assuming you have the testMap already defined
// testMap: Map<string, any>

// Step 1: Get the selected key from the dropdown (replace 'selectedKey' with the actual selected key)
const selectedKey = 'someKey';

// Step 2: Retrieve the corresponding object from the map
const selectedObject = testMap.get(selectedKey);

// Step 3: Update the "name" property of the object
if (selectedObject) {
  selectedObject.name = selectedKey;
} else {
  // Handle the case when the selected key is not found in the map
  console.error('Selected key not found in the map!');
}

// Step 4: Set the updated object back into the map using the same key
testMap.set(selectedKey, selectedObject);

// Now, the "name" property of the selected object in the map should be updated to the selected key.