Why is my Gui not becoming less transparent and showing my text?

The problem is that the GUI may not have loaded when the event fires. To fix this, use :WaitForChild()

game.Players.PlayerAdded:connect(function(plr)
	local name = plr.Name   
	local gui = plr.PlayerGui:WaitForChild("ScreenGui"):WaitForChild("TextLabel") --// the problem gets fixed here
	for i = 0.1,0.5,0.1 do
		gui.BackgroundTransparency = i
		wait(0.01)
	end
	gui.Text = name .. "has entered the game!"
end)

Edit:

I have optimised your script a bit, the main change being the for loop; it makes it much faster to accomplish what you want to do.

For loops like the one I am using have a third parameter, it being the 'step' (defaulting to 1). This script will run from 0.1 to 0.5 increasing by 0.1 every time.

Tip:

Use Tab, not Space. Space is inconsistent and thus very annoying.

As a side note, this script only shows the player joined notification on the player that joined; therefore this feature is mostly obsolete, at least for what it is normally used for.

If you want, I can expand my answer and break the solution down for you?

Hope I helped!

~TDP