This can not be done with an array because array items do not have names. The variable names are not kept when constructing the array, only their values.

It can be done with an object, and then you can use Object.entries to iterate over the contents of the object and get both the key and the value for each item:

var date = '1/1/22';
var time = '5:00'
var name = 'some name';
var number = '123-456-7890';

var obj = { date, time, name, number };

for (var [key, value] of Object.entries(obj))
  console.log(key + ": " + value)

A final note: the ordering of items as returned by Object.entries() is not guaranteed.

Another option is to put objects with a single named property into an array. This way the ordering of items is guaranteed, and item names are available using Object.keys():

var date = '1/1/22';
var time = '5:00'
var name = 'some name';
var number = '123-456-7890';

var arr = [ { date }, { time }, { name }, { number } ];

for (var item of arr) {
  // We have knowledge that every object has only 1 property, get its name:
  var key = Object.keys(item)[0];
  console.log(key + ": " + item[key]);
}

I think your best option is to use a 2-dimensional array. Here is a code snippet (I copied this from a MacBook, so hopefully it formats ok):

        function getVarAndValArray() {

        var date = '1/1/22';
        var time = '5:00'
        var name = 'some name';
        var number = '123-456-7890';

        //Create two-dimensional array
        let arr = [];
        arr[0] = [];    //date
        arr[1] = [];    //time
        arr[2] = [];    //name
        arr[3] = [];    //number
        //-----------------------------------

        //Insert variables names and values
        //Date
        arr[0][0] = 'date';         //variable
        arr[0][1] = '1/1/22';       //value
        //Time
        arr[1][0] = 'time';         //variable
        arr[1][1] = '5:00';         //value
        //Name
        arr[2][0] = 'name';         //variable
        arr[2][1] = 'some name';    //value
        //Number
        arr[3][0] = 'number';       //variable
        arr[3][1] = '123-456-7890'; //value
        //------------------------------------

        return arr;
    }

    //Output the results
    var arr = getVarAndValArray();
    var text = '';
    text += arr[0][0].toUpperCase() + ": " + arr[0][1] + "\n";
    text += arr[1][0].toUpperCase() + ": " + arr[1][1] + "\n";
    text += arr[2][0].toUpperCase() + ": " + arr[2][1] + "\n";
    text += arr[3][0].toUpperCase() + ": " + arr[3][1] + "\n";
    alert(text);