Transferring Variable through Remote Event?

The server will automatically detect the player who fired this remote event.

local Player = game.Players.LocalPlayer

ClaimButton.MouseButton1Click:Connect(function()
    if Claimable.Value == true then
        print("fired")
        Client2Server.Claim:FireServer(Player)
    else
        game.SoundService.Fart:Play()--Because why not?
    end
end)

This means in the server script, you will add one argument which is going to be the player

local Claim = game.ReplicatedStorage.Client2Server.Claim

local ClaimList = {
    ["Claim1"] = "";
    ["Claim2"] = "";
    ["Claim3"] = "";
    ["Claim4"] = "";
    ["Claim5"] = "";
    ["Claim6"] = "";
    ["Claim7"] = "";
    ["Claim8"] = "";
    ["Claim9"] = "";
    ["Claim10"] = "";
    ["Claim11"] = "";
    ["Claim12"] = "";
    ["Claim13"] = "";
    ["Claim14"] = "";
    ["Claim15"] = "";
    ["Claim16"] = "";}


local TotalClaims = 0

Claim.OnServerEvent:Connect(function(Player) --This argument is the player who fired this remote event
    print("we got it boys")
    for i,v in pairs(ClaimList)do
        print("in dat list")
        if v == "" then
            v = Player.Name
            print(Player,"is",v)
        end
    end
end)

I hope this helped, if it didn't please forgive me, I am not extremely professional myself.