make a gui visible only for the players with their names written on the table?

So, you were on the right track by using a pairs loop, but you weren't checking each entry of your "admins" table in it.

"if v.Name == admins then"

That line will try to compare each name to the table itself, which of course won't work for what you're trying to do.

Here's how I would implement it:

local Players = game:GetService("Players")
local adminList = {"PicoTheRiko", "toxa_pas"} -- I'd recommend using player's UserId's, as opposed to using their Username, because if they change their name then you'll have to update this list.

local function checkForAdmins()
    local players = Players:GetPlayers()
    for _, Player in pairs(players) do
        local foundAdmin = false; -- used to track whether or not this Player is an admin 
        for _, admin in pairs(adminList) do
            if Player.Name == admin then
                foundAdmin = true
                break -- breaks the admin loop
            end
        end
        if foundAdmin then -- checks to see if the previous loop changed the foundAdmin bool at all
            print(Player.Name .. " is an admin.")
            -- add the function that will show the admin only stuff here
        else
            print(Player.Name .. " is not an admin.")
            -- add the function that will hide the admin only stuff here
        end
    end
end

while true do -- will run our checkForAdmins function every 3 seconds.
    wait(3)
    checkForAdmins()
end

I think it's because you're not referrencing the table position, wich can be done like so:

admins[1] -- position 1 wich is "PicoTheRiko"
admins[2] -- position 2 wich is "toxa_pas"

So with that, we can make your script to print

local admins = {"PicoTheRiko", "toxa_pas"} 

local player = game.Players:GetChildren()

for i, v  in pairs(player) do
    if v.Name == admins[1] or v.Name == admins[2] then
        print("found")
    else
        print("not")
    end
end

Now, to make the gui appear, we can do it like so:

local admins = {"PicoTheRiko", "toxa_pas"} 

local player = game.Players:GetChildren()

for i, v  in pairs(player) do
    if v.Name == admins[1] or v.Name == admins[2] then
        game.Players.LocalPlayer:WaitForChild("screenGuiNameHere").Enabled = true
    end
end

Test it out, if it still doesn't work, you can do a loop with a wait() to run that script every few seconds.