How would I use a function to start a while loop?

I fixed the script and this works

function onClick()
    while true do
        game.Players.LocalPlayer.leaderstats.Score.Value = game.Players.LocalPlayer.leaderstats.Score.Value + 1
        local str =  game.Players.LocalPlayer.leaderstats.Score.Value
        local str1 = "Your income: "
        game.Players.LocalPlayer.PlayerGui.ScreenGui.Frame.TextButton.Text = str1..str
        wait(1)
    end
end

script.Parent.MouseButton1Click:connect(onClick)

Oh, then you need an event. I prefer anonymous functions when I do events, but you can do it with a normal function just as easily. I will do a normal function here, since that's what you asked.

function onClick()
    while true do
        stats.Score.Value = stats.Score.Value + 1
        local str = stats.Score.Value
        local str1 = "Your income: "
        player.PlayerGui.ScreenGui.Frame.TextButton.Text = str1..str
        wait(1)
    end
end

script.Parent.MouseButton1Down:connect(onClick)