Getting a player name (test mode) - attempt to index field localplayer (a nil value)?

Hi

I'm making a very simple race against the clock game. The player has to run a very simple course, and they see their time updated every second. There is a part on the finish line which, when they touch, can tell them their finish time.

There is a script in the finish line part which holds a variable called raceactive. This is set to false when you hit the finish part, but before then it updates the elapsed time (in seconds) on a screengui in the startergui.

The difficulty I am having is finding the player name so I can refer to the screengui. If I use the following, then I get a message "attempt to index field 'LocalPlayer' (a nil value)"

local player=game.Players.LocalPlayer.Name

However if I hard code my username (see below) then the script does what I would like it to do

local player=game.Players.myname

Grateful for any help people can offer. The whole script is below.

Many Thanks

Chris

-- Keep track of time the racer has been running

local timepassed=0  -- timer variable
local finishLine=script.Parent -- finsih line part
local raceactive=true -- testing if race is active
-- local timergui=game.StarterGui.TimerGui.TimerText -- The Gui for the timer
-- print (timergui.Text)
-- wait(2)
-- print (timergui)
-- timergui.text="Changing the text"

-- Function which is run at the end of the race
local function finish()
    if raceactive==true then
        print ("You finished in "..timepassed.." seconds")
        raceactive=false -- sets flag to end the race




    end

end

-- Function for when the finish line is touched

local function partTouched(otherpart)
    local character=otherpart.Parent
    local humanoid=character:FindFirstChildWhichIsA("Humanoid")
    if humanoid then finish()

    end
end

-- When finishline is touched, call the partTouched function
finishLine.Touched:Connect(partTouched)

-- The race timer




while raceactive==true do
    wait(1)
    timepassed=timepassed+1 -- Increment the timer
    -- local players=game:GetService("Players").LocalPlayer
    local   player=game.Players.LocalPlayer.Name
    print (player)
    -- local player=game.Players.redchris999
    local PlayerUI = player:WaitForChild("PlayerGui")
    local ScreenGui = PlayerUI:WaitForChild("ScreenGui");
    local TextLabel = ScreenGui:WaitForChild("TimerText");
    -- print (TextLabel.Text)
    TextLabel.Text=timepassed.." seconds have passed "..player.Name
end