Generating a random number in Swift

It really depends on how much casting you want to avoid. You could simply wrap it in a function:

func random(max maxNumber: Int) -> Int {
    return Int(arc4random_uniform(UInt32(maxNumber)))
}

So then you only have to do the ugly casting once. Everywhere you want a random number with a maximum number:

let r = random(max: _names.count)
let name: String = _names[r]

As a side note, since this is Swift, your properties don't need _ in front of them.

I really like using this extension

extension Int {
    init(random range: Range<Int>) {

        let offset: Int
        if range.startIndex < 0 {
            offset = abs(range.startIndex)
        } else {
            offset = 0
        }

        let min = UInt32(range.startIndex + offset)
        let max = UInt32(range.endIndex   + offset)

        self = Int(min + arc4random_uniform(max - min)) - offset
    }
}

Now you can generate a random Int indicating the range

let a = Int(random: 1...10) // 3
let b = Int(random: 0..<10) // 6
let c = Int(random: 0...100) // 31
let d = Int(random: -10...3) // -4