I thought const variables were immutable, how do we use const for this and are able to change the name property?

// The following line will create an object called person
const person;
// This object is now create and cannot be modified because of the const
// if you do this  you will get an error because the person object has been already create and is immutable
person = 'me';
// This is the right way to do this
const person = 'me';
// Now you have an object that is immutable and is referring 'me'.

// As for the video that you are referring to:
const person = {
    name: 'Edward',
    city: 'New York',
    age: 37,
    isStudent: true,
    skills: ['Javascript', 'HTML', 'CSS']
};
// in this case the object person has been create and the object itself is immutable,
// but this object also has properties like, name, city, age, isStudent, skills.
// Those properties are mutable, you can change the properties but not the object itself.
// Here is how to change the properties

person.name = 'Steve';
person.city = 'London';

// You can also add more properties to the object

person.position = 'Lead Programmer';
person.description = 'I like to code';

// Here is what you can't do because the person object has already been declared above
const person = 'me';
const person = {
    name: 'Mike',
    age: 20
};