Despite no errors being shown in the output, this script that changes Text isn't working, help?

You are changing the text of the textlabel in starter gui, not the one of the player,

local TextLabel = game.StarterGui.GameplayGui.PlayerInfo.PlayerName
local Player = game.Players.LocalPlayer
local UserName = Player.Name

game.Players.PlayerAdded:connect(function()
    TextLabel.Text = UserName--TextLabel is game.StarterGui etc
end)

If you change the startergui one, it will show the players name when they refresh their gui, or when a new player joins, their gui will say the old username

What I think you want to do is change the text of the player that joined textlabel, to do that you would just do this instead,

local TextLabel = game.StarterGui.GameplayGui.PlayerInfo.PlayerName

game.Players.PlayerAdded:connect(function(p)--P is equal to the player who joined
    p.PlayerGui.GameplayGui.PlayerInfo.PlayerName.Text = p.Name--Change the destination of the statements for your own script
end)

Hope this helped, if it did, accept the answer it gives us both rep!