How Can I Print The First Player's Name?

How Can I Print the First/Second Player's name on the table?

local playersInRedRoom = {}
clickJoinGreenRoom.MouseClick:Connect(function(player)
		if #playersInRedRoom < 2 then
		table.insert(playersInRedRoom, player.Name)

print("The Player "..playersInRedRoom[2].Player.Character.Name.."Two Got a Point!")

From what I see, you're inserting the player's name into the table (a string), but when you call it back, you treat it as a player instance.

local playersInRedRoom = {}
clickJoinGreenRoom.MouseClick:Connect(function(player)
        if #playersInRedRoom < 2 then
        	table.insert(playersInRedRoom, player.Name)
		print("The Player "..playersInRedRoom[2].."Two Got a Point!")
	end
end)

Treating it as a string should work. (I also noticed that a couple ends was missing, so I added those.)

If the if statement is true, then that means there's 0 or 1 values in variable playersInRedRoom. So when you add the second or first name, you either get two or one value in variable playersInRedRoom. I would use #playersInRedRoom to get the latest value.

local playersInRedRoom = {}
clickJoinGreenRoom.MouseClick:Connect(function(player)
	if #playersInRedRoom < 2 then
		table.insert(playersInRedRoom, player.Name)
		print("The Player "..playersInRedRoom[#playersInRedRoom].."Two Got a Point!")
	end
end)