Why an ObservedObject array is not updated in my SwiftUI application?

You can use a struct instead of a class. Because of a struct's value semantics, a change to a person's name is seen as a change to Person struct itself, and this change is also a change to the people array so @Published will send the notification and the View body will be recomputed.

import Foundation
import SwiftUI
import Combine

struct Person: Identifiable{
    var id: Int
    var name: String

    init(id: Int, name: String){
        self.id = id
        self.name = name
    }

}

class Model: ObservableObject{
    @Published var people: [Person]

    init(){
        self.people = [
            Person(id: 1, name:"Javier"),
            Person(id: 2, name:"Juan"),
            Person(id: 3, name:"Pedro"),
            Person(id: 4, name:"Luis")]
    }

}

struct ContentView: View {
    @StateObject var model = Model()

    var body: some View {
        VStack{
            ForEach(model.people){ person in
                Text("\(person.name)")
            }
            Button(action: {
                self.mypeople.people[0].name="Jaime"
            }) {
                Text("Add/Change name")
            }
        }
    }
}

Alternatively (and not recommended), Person is a class, so it is a reference type. When it changes, the People array remains unchanged and so nothing is emitted by the subject. However, you can manually call it, to let it know:

Button(action: {
    self.mypeople.objectWillChange.send()
    self.mypeople.people[0].name="Jaime"    
}) {
    Text("Add/Change name")
}

I think there is a more elegant solution to this problem. Instead of trying to propagate the objectWillChange message up the model hierarchy, you can create a custom view for the list rows so each item is an @ObservedObject:

struct PersonRow: View {
    @ObservedObject var person: Person

    var body: some View {
        Text(person.name)
    }
}

struct ContentView: View {
    @ObservedObject var mypeople: People

    var body: some View {
        VStack{
            ForEach(mypeople.people){ person in
                PersonRow(person: person)
            }
            Button(action: {
                self.mypeople.people[0].name="Jaime"
                //self.mypeople.people.append(Person(id: 5, name: "John"))
            }) {
                Text("Add/Change name")
            }
        }
    }
}

In general, creating a custom view for the items in a List/ForEach allows each item in the collection to be monitored for changes.

For those who might find it helpful. This is a more generic approach to @kontiki 's answer.

This way you will not have to be repeating yourself for different model class types

import Foundation
import Combine
import SwiftUI

class ObservableArray<T>: ObservableObject {

    @Published var array:[T] = []
    var cancellables = [AnyCancellable]()

    init(array: [T]) {
        self.array = array

    }

    func observeChildrenChanges<T: ObservableObject>() -> ObservableArray<T> {
        let array2 = array as! [T]
        array2.forEach({
            let c = $0.objectWillChange.sink(receiveValue: { _ in self.objectWillChange.send() })

            // Important: You have to keep the returned value allocated,
            // otherwise the sink subscription gets cancelled
            self.cancellables.append(c)
        })
        return self as! ObservableArray<T>
    }


}

class Person: ObservableObject,Identifiable{
    var id: Int
    @Published var name: String

    init(id: Int, name: String){
        self.id = id
        self.name = name
    }

} 

struct ContentView : View {
    //For observing changes to the array only. 
    //No need for model class(in this case Person) to conform to ObservabeObject protocol
    @ObservedObject var mypeople: ObservableArray<Person> = ObservableArray(array: [
            Person(id: 1, name:"Javier"),
            Person(id: 2, name:"Juan"),
            Person(id: 3, name:"Pedro"),
            Person(id: 4, name:"Luis")])

    //For observing changes to the array and changes inside its children
    //Note: The model class(in this case Person) must conform to ObservableObject protocol
    @ObservedObject var mypeople: ObservableArray<Person> = try! ObservableArray(array: [
            Person(id: 1, name:"Javier"),
            Person(id: 2, name:"Juan"),
            Person(id: 3, name:"Pedro"),
            Person(id: 4, name:"Luis")]).observeChildrenChanges()

    var body: some View {
        VStack{
            ForEach(mypeople.array){ person in
                Text("\(person.name)")
            }
            Button(action: {
                self.mypeople.array[0].name="Jaime"
                //self.mypeople.people.append(Person(id: 5, name: "John"))
            }) {
                Text("Add/Change name")
            }
        }
    }
}