How to make a GUI show up to a specific player?

A way how you could do it and easiest way would probably to already have the Gui made and put it in StarterGui, but change the Visible property of it to false. Then run a code to see if it's the person it's looking for, and then change the Visible to true. Such as:

game.Players.PlayerAdded:connect(function(player)
    if player.Name == "BannedNameHere" then
        player.PlayerGui.BannedGUI.Visible = true
    end
end)

Or if you had a string of players who are banned, you could put them in a table and then run through it:

bannedList = {"1x1x1x1", "Telamon", "BannedName"}

game.Players.PlayerAdded:connect(function(player)
    for i, v in pairs(bannedList) do
        if player.Name == v then
            player.PlayerGui.BannedGUI.Visible = true
        end
    end
end)

If this wasn't specific enough, let me know!