Adding "self" to the initial value inside of the Initialization method

Yes that would be fine. you can use self in front of the property name, however it is not necessary. you only need to use self to distinguish a property from a parameter when there is a naming conflict or ambiguity. If there is no ambiguity, it is conventional to omit self

the Swift eBook states:

In practice, you don’t need to write self in your code very often. If you don’t explicitly write self, Swift assumes that you are referring to a property or method of the current instance whenever you use a known property or method name within a method. This assumption is demonstrated by the use of count (rather than self.count) inside the three instance methods for Counter.

The main exception to this rule occurs when a parameter name for an instance method has the same name as a property of that instance. In this situation, the parameter name takes precedence, and it becomes necessary to refer to the property in a more qualified way. You use the self property to distinguish between the parameter name and the property name.

Here, self disambiguates between a method parameter called x and an instance property that is also called x:

struct Point {
    var x = 0.0, y = 0.0
    func isToTheRightOfX(x: Double) -> Bool {
        return self.x > x
    }
}