How do I create a Set of custom objects (Swift)?

To make set of Person you need to make it conform to Equatable and Hashable protocols:

class Person: Equatable, Hashable {
    var Id: Int
    var Name: String

    init(id: Int, name: String?) {
        self.Id = id
        self.Name = name ?? ""
    }

    var hashValue: Int {
        get {
            return Id.hashValue << 15 + Name.hashValue
        }
    }
}

func ==(lhs: Person, rhs: Person) -> Bool {
    return lhs.Id == rhs.Id && lhs.Name == rhs.Name
}

Then you can use set of persons like this:

var set = Set<Person>()
set.insert(Person(id: 1, name: "name"))