How can I reference the model I created without renaming it?

Your error was here:

local player = game.Players.PlayerAdded

The PlayerAdded event fires when a player enters the game, you cannot reference like a value. I will return a modified version of your script and you tell me if it works please.

local function addRequiredParts(player)
    local playerID = player.UserId
    local Location = game.ReplicatedStorage.playerData.playerID.givenValues
    local tempVar = Instance.new("BoolValue")
    tempVar.Name = "newPlyr"
    tempVar.value = false
    tempVar.Parent = Location
    tempVar = nil
    local tempvar = Instance.new("NumberValue")
    tempvar.Name = "forceMastery"
    tempvar.value = nil
    tempvar.Parent = Location
    tempvar = nil
    local tempvar = Instance.new("NumberValue")
    tempvar.Name = "forceEndurance"
    tempvar.value = 100
    tempvar.Parent = Location
    tempvar = nil
    local tempvar = Instance.new("BoolValue")
    tempvar.Name = "usingForce"
    tempvar.value = false
    tempvar.Parent = Location
    tempvar = nil
    local tempvar = Instance.new("NumberValue")
    tempvar.Name = "forceSrength"
    tempvar.Value = nil
    tempvar.Parent = Location
    tempvar = nil
end



game.Players.PlayerAdded:Connect(function(player)
    local newData = Instance.new("Model") 
    local playerID = player.UserId
    newData.Name = (playerID)
    newData.Parent = game.ReplicatedStorage.playerData
    local playerValues = Instance.new("Model")
    playerValues.Name = "givenValues"
    playerValues.Parent = newData
    addRequiredParts(player)
end)

Again, if this does work, please consider making this an accepted answer.