[voraa]

Надо так

let Person =function(name,age,gender){
        this.name = name;
        this.age = age;
        this.gender = gender;
        return this;
    };
Person.prototype.greet= function(){
       console.log("My name is " + this.name);
    };
var tom = new Person("Вася",18,"female");
tom.greet();

Либо так

class Person {
    constructor (name,age,gender){
        this.name = name;
        this.age = age;
        this.gender = gender;
        return this;
    }
    greet (){
       console.log("My name is " + this.name);
    }
}

var tom = new Person("Вася",18,"female");
tom.greet();

В крайнем случае (непонятно, зачем) так

let Person = {
    constructor:function(name,age,gender){
        this.name = name;
        this.age = age;
        this.gender = gender;
       this.greet = Person.greet;
        return this;
    },
    greet: function(){
       console.log("My name is " + this.name);
    }
};
 
var tom = new Person.constructor("Вася",18,"female");
tom.greet();