Authorization script, it not works for both name why?

Let's "unroll" the for loop. For loops just do something once per thing in the container. So your code is currently equivalent to

do -- iteration 1
    local v = "NiniBlackJackQc"
    if player.Name == v or player.UserId == game.CreatorId then
        script.Parent:Destroy()
        GameSound()
        print("Administrator: "..player.Name, "Administrator Id: "..player.UserId)
        return; -- This stops the loop from running anymore.
    else
        Character:Destroy()
        Instance.new("BlurEffect",workspace.CurrentCamera)
        IntroSound()
        print("Player: "..player.Name, "Player Id: "..player.UserId)
        return;
    end
end

do -- iteration 2
    local v = "DAHUI84"
    if player.Name == v or player.UserId == game.CreatorId then
        script.Parent:Destroy()
        GameSound()
        print("Administrator: "..player.Name, "Administrator Id: "..player.UserId)
        return; -- This stops the loop from running anymore.
    else
        Character:Destroy()
        Instance.new("BlurEffect",workspace.CurrentCamera)
        IntroSound()
        print("Player: "..player.Name, "Player Id: "..player.UserId)
        return;
    end
end

Notice that you're never going to get passed the first loop: you unconditionally return having made a decision based on only the first name in the list.

Here is the code you meant to write. We can define isAuthorized later:

local Authorization = {"NiniBlackJackQc","DAHUI84"}

local player = game:GetService("Players").LocalPlayer
repeat wait() until player.Character

local Character = player.Character

if isAuthorized() then
    script.Parent:Destroy()
    GameSound()
    print("Administrator: "..player.Name, "Administrator Id: "..player.UserId)
else
    Character:Destroy()
    Instance.new("BlurEffect",workspace.CurrentCamera)
    IntroSound()
    print("Player: "..player.Name, "Player Id: "..player.UserId)
end

This clearly doesn't have logic bugs, because it says to do exactly what you want (notice that since there's no more code there's no need for returns either)

isAuthorized is simple:

function isAuthorized()
    if player.UserId == game.CreatorId then
        return true
    end

    for _, name in pairs(Authorization) do
        if name == player.Name then
            return true
        end -- we can't say "else" because there are more names
    end
end

I'm not an expert at scripting but I would try to change player to players because it is more than 1 player or I will try to make 2 separate script and make it with 1 of the names each instead of 2 times in one script. Hope I helped :) Merry Christmas!