Give Count of number of character accrued in a String using JavaScript

The variable i in for...in represents the key (or index in the case of an array). Since you don't need the index, use for...of instead:

var name = "Interesting";
name = name.replace(/ +/g, "").toLowerCase();
// name = name.split('').join(''); // remove - this doesn't do anything
var letter_count = {}

for(var i of name){
   if (!(i in letter_count)){
    letter_count[i] = 1;
   }
  else {
   letter_count[i] += 1;
  }
}

console.log(letter_count);

If you need a fancy functional programming approach:

const letterCount = name.toLowerCase().split('').reduce((acc, curr) => {
    acc[curr] ? acc[curr]++ : acc[curr] = 1;
    return acc;
}, {});

console.log(letterCount);

You can find the documentation of reduce function here: link

I think you were a little confused with how to use the i variable. It is actually the index of the character, not the character. To get the character, you need to use var c = name[i];

var name = "Interesting";
name = name.replace(/ +/g, "").toLowerCase();
name = name.split('').join('');
var letter_count = {}

for(var i in name){
   var c = name[i];
   if (!(c in letter_count)){
    letter_count[c] = 1;
   }
  else {
   letter_count[c] += 1;
  }
}

console.log(letter_count);

There are couple of unnecessary and mistaken things in your code and I put them in comments inside code

var name = "Interesting";
// you do not need to do this name = name.replace(/ +/g, "").toLowerCase();
name = name.toLowerCase();
// nor this name = name.split('').join('');
var letter_count = {}

for(var i in name){
   var character = name[i]; // here we set the value of character to be letter from name
   if (!(character in letter_count)){
    letter_count[character] = 1; // here we are giving it initial value if it is not found so far
   }
  else {
   letter_count[character] += 1; // here we are giving it value if it already exists
  }
}

console.log(letter_count);