Two warnings which don't seem to be normal?

Your problem is that your script thinks that "Name" is the property Name inside the BillboardGui. To fix this, simply rename your TextLabel into "name" instead of "Name". Then, change all of the "Name"s in the script into "name"s:

--// variables //--
local gui = game:GetService("ServerStorage"):WaitForChild("BillboardGui")

game.Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function(char)
        if char.Head:FindFirstChild("BillboardGui") then
            print("BillboardGui is already inserted")
        else
            local clone = gui:Clone()
            clone.Frame.name.Text = player.Name
            clone.Frame.name.TextColor3 = Color3.fromRGB(100,0,0)
            clone.Parent = game.Workspace:WaitForChild(player.Name).Head
        end
    end)
end)

Hope this helps!

Edit: Another error - which is irrelevant to your question - can also be seen. You are saying Color3.RGB on line 11, but this isn't a thing. You must use Color3.fromRGB. I edited the script above.