Your filter for the result is wrong. You should be using the "object.spaceName" instead of just "name" as you're looping through an array of objects and not just strings

// So this line:
const results = arrayObjTwo.filter(name => !object1Names.includes(name));

// Should be:
const results = arrayObjTwo.filter(object => !object1Names.includes(object.spaceName));

// And you have a typo:
const object1Names = arrayObjOne.map(obj => obj.Name);

// Should be like so as keys and properties are case-sensitive:
const object1Names = arrayObjOne.map(obj => obj.name);

So this should all be:

const arrayObjOne = [{
          countryCode: "US",
          description: " Backyard of home",
          id: "1234",
          location: "US",
          name: "Backyard",
          }]
// Array Object 2
const arrayObjTwo =[
    { description: "Backyard of home", spaceName: "Backyard" },
    { description: "Frontyard of home", spaceName: "Frontyard"},
]
const object1Names = arrayObjOne.map(obj => obj.name); // for caching the result
const results = arrayObjTwo.filter(object => !object1Names.includes(object.spaceName));
console.log(results);

You're close!

You have capitalized names in your map-statement, but javascript is case-sensitive, so the field you're looking up "Name", does not exist, and as such your "object1Names" returns undefined.

You should be looking up obj.name

You also need to compare it to the arrayObjTwo's "spaceName"-field, not the entire object.

Here's your code with these small changes:

const arrayObjOne = [{
          countryCode: "US",
          description: " Backyard of home",
          id: "1234",
          location: "US",
          name: "Backyard",
          }]
// Array Object 2
const arrayObjTwo =[
    { description: "Backyard of home", spaceName: "Backyard" },
    { description: "Frontyard of home", spaceName: "Frontyard"},
]
const object1Names = arrayObjOne.map(obj => obj.name); // for caching the result
const results = arrayObjTwo.filter(obj => !object1Names.includes(obj.spaceName));
console.log(results);

Do you need this?

const arr1 = [{
          countryCode: "US",
          description: " Backyard of home",
          id: "1234",
          location: "US",
          name: "Backyard",
          }]
// Array Object 2
const arr2 =[
    { description: "Backyard of home", spaceName: "Backyard" },
    { description: "Frontyard of home", spaceName: "Frontyard"},
]
const names = arr1.map(item => item.name); // for caching the result
console.log(names);
const res = arr2.filter(item => !names.includes(item.name));
console.log(res);