You're using the wrong equals here:
if (name="John" && "Penny" && "Pat")
Change it to
if (name === "John" || name === "Penny" || name === "Pat")
You're also setting name incorrectly:
var name = ("John" & "Penny" & "Pat")
should be
var name = ["John", "Penny", "Pat"];
(if you want an array.) (Though you're overwriting it in the next line, so why ever set it like that in the first place?).
Finally, it's bad practice to use document.write, try console.log instead.
To sum up so far:
var name = prompt("What is the student name?");
if (name === "John" || name === "Penny" || name === "Pat") {
console.log(name + " has one free hour of lessons.");
} else {
console.log(name + " doesn't have any free lessons.");
}
As noted in the comments, this gets difficult when you add more users. Instead, let's store the users who have a free hour in an array (thus, adding new students is easy, just add them to the array):
var haveFreeHour = ["John", "Penny", "Pat"];
Then, we can use indexOf in the if statement:
var haveFreeHour = ["John", "Penny", "Pat"];
var name = prompt("What is the student name?");
if (haveFreeHour.indexOf(name) > -1) {
console.log(name + " has one free hour of lessons.");
} else {
console.log(name + " doesn't have any free lessons.");
}
Play with this at JSFiddle