Text is a view, and first, you never call winOrLose(), so nothing ever happens to alertMessage and it remains at its initialised value of "". (Note - convention is that functions always start with a lowercase letter - so winOrLose() not WinOrLose())

The easiest way around this is to add the .onAppear function call extension to Text.

Second, as you already set the value of alertMessage, which is a @State variable, then there is no need for the return statement. In fact this would cause a problem when calling the .perform: action in the .onAppear.

I have also given a couple of examples (commented out) of a ternary version of the if statement, that could be used here as an alternative method to setting alertMessage.

struct ContentView: View {
    @State var shouldWin = Int.random(in: 0...2)
    @State var alertMessage = ""
    @State var number = Int.random(in: 0...2)

    func winOrLose() {
        if number == shouldWin {
            alertMessage = "You need to win this round!"
        }
        else {
            alertMessage = "You need to lose this round"
        }

//        alertMessage = (number == shouldWin ?
//            "You need to win this round!" :
//            "You need to lose this round")

//        alertMessage = "You need to \(number == shouldWin ? "win" : "lose") this round!"
    }

    var body: some View {

        Text(alertMessage)
            .onAppear(perform: winOrLose)
    }
}