You can filter genres using genre_ids and then map the specific values

function filterGenres(genres, ids) {
    return genres
        .filter((genre) => ids.indexOf(genre.id) != -1)
        .map((genre) => genre.name)
}

or alternatively use the reduce function

function filterGenres(genres, ids) {
    return genres.reduce((results, genre) => {
        if(ids.indexOf(genre.id) != -1) {
            results.push(genre.name);
        }
        return results;
    }, []);
}

The below may be one possible solution to achieve the desired objective.

Code Snippet

const getNames = (ids, objects) => (
  ids.map(el => (
    objects.find(
      ({id}) => id === el
    )?.name
  ))
);

// below will be better in performance
// but the names returned will be ordered based on 'genres' array
//  objects.filter(({id}) => ids.some(el => el === id))
//  .map(({name}) => name)


const genres = [
  { id: 28, name: "Action" },
  { id: 12, name: "Adventure" },
  { id: 16, name: "Animation" },
  { id: 35, name: "Comedy" },
  { id: 80, name: "Crime" },
  { id: 99, name: "Documentary" },
  { id: 18, name: "Drama" },
  { id: 10751, name: "Family" },
  { id: 14, name: "Fantasy" },
  { id: 36, name: "History" },
  { id: 27, name: "Horror" },
  { id: 10402, name: "Music" },
  { id: 9648, name: "Mystery" },
  { id: 10749, name: "Romance" },
  { id: 878, name: "Science Fiction" },
  { id: 10770, name: "TV Movie" },
  { id: 53, name: "Thriller" },
  { id: 10752, name: "War" },
  { id: 37, name: "Western" },
];

const genre_ids = [10752, 10770, 18, 12];

console.log(getNames(genre_ids, genres));

Explanation

• A new method getNames is used to obtain the result
• For each id in genre_ids array
• Find if there is an entry in genres (by matching the id prop)
• If found, return the name prop from the matched genres element
• And the resulting array is returned (implicitly)

Commented-out method:

• Filter the genres and destructure to obtain just the id
• Check if the id is present in the genre_ids array
• If yes, use .map to destructure just the name
• And this resulting array of names is returned (implicitly)

This method returns in a different order (based on the genres array).

are you trying something like this -

let genre_names = new Array();
for(let i=0; i<genre_ids.length; i++) {
   var a = genres.find(x=>x.id == genre_ids[i]);
   if (!!a)
     genre_names.push(a.name);
}
console.log(genre_names);

resulting with [War,Tv Movies, drama, Adventure] ?