Try this. You can improve this further by performance wise, if you work around a bit.

  var data = {
 "Test": "1",
 "value": [
    {
        "NAME": "ABCD",
        "ID": "1234",
        "ACTIVE": "true"
    },
    {
        "NAME": "ABCD",
        "ID": "1234",
        "ACTIVE": "true"
    },
    {
        "NAME": "ABCD",
        "ID": "1234",
        "ACTIVE": "true"
    },
    {
        "NAME": "EFGH",
        "ID": "5678",
        "ACTIVE": "true"
    },
    {
        "NAME": "IJKL",
        "ID": "91011",
        "ACTIVE": "true"
    }
   ]
 };
 var objArray = data.value;
 var duplicates = []; // duplicates will be stored here.
 for(var i=0, iLen = objArray.length; i<iLen;i++){
    var obj = objArray[i];
        var filtered = objArray.filter(function(arrVal) {
        return arrVal.NAME === obj.NAME && arrVal.ID === obj.ID ;
    });
    var dup = obj.NAME + ":" + obj.ID;
    if(filtered.length>=3 && duplicates.indexOf(dup) < 0) {
        duplicates.push(dup);
    }

 }

this questuon was answered multiple times on SO. You create array from the json and compare the elements of the array.

How to remove all duplicates from an array of objects?

According to your sample output I believe it's "at least 3 times" rather than "more than 3 times".

Below snippet can product the expected output with the sample data.

const data = {
"Test": "1",
"value": [
    {
        "NAME": "ABCD",
        "ID": "1234",
        "ACTIVE": "true"
    },
    {
        "NAME": "EFGH",
        "ID": "5678",
        "ACTIVE": "true"
    },
    {
        "NAME": "EFGH",
        "ID": "5678",
        "ACTIVE": "true"
    },
    {
        "NAME": "EFGH",
        "ID": "5678",
        "ACTIVE": "true"
    },
    {
        "NAME": "ABCD",
        "ID": "1234",
        "ACTIVE": "true"
    },
    {
        "NAME": "ABCD",
        "ID": "1234",
        "ACTIVE": "true"
    },
    {
        "NAME": "IJKL",
        "ID": "91011",
        "ACTIVE": "true"
        }
    ]
};

const occurrence = {}; // key: count
const result = [];
for (const item of data.value) {
  const key = `${item.NAME}:${item.ID}`;
  occurrence[key] = (occurrence[key] || 0) + 1;
  if (occurrence[key] >= 3) {
    result.push(key);
  }
}

console.log(result);