How do I make this script let all the player type the command instead of specific players?

All you have to do is remove the for loop which checks the name of the player against the table. If you aren't using the table, you can remove that too.

local current_map; --// Usage of local variables is recommended, and you can omit the '= nil' when the value is nil.

game.Players.PlayerAdded:connect(function(player)
    player.Chatted:connect(function(chatmsg)
        if chatmsg:sub(1,4) == "spawn/" then
            local map = chatmsg:sub(5, chatmsg:len())
            if game.Lighting:FindFirstChild(map) then
                if current_map ~= nil then
                    current_map.Parent = game.Lighting
                end
                game.Lighting[map].Parent = game.Workspace
                current_map = game.Workspace[map]
            end
        end
    end)
end)

I did it for you this time, but for future reference, please properly indent your code; it makes it easier for anyone who wants to help you out to read your code, and makes it easier for you to fix any potential errors.

Hope this helped.

You simply have to remove the part where it checks the player name. Looks like you don't have much scripting knowledge so I'll do this for you.

local current_map

game.Players.PlayerAdded:connect(function(player)
    player.Chatted:connect(function(chatmsg)
        if chatmsg:sub(1,4) == "spawn/" then
            local map = game.Lighting:FindFirstChild(chatmsg:sub(5))
            if map then
                if current_map then
                    current_map.Parent = game.Lighting
                end 
                map.Parent = workspace
                current_map = map
            end
        end
    end)
end)

I also did some optimization. I recommend using ServerStorage over lighting but I don't want to break your game myself lol. Later