How do I get the player that just joined's name in a local script from FireAllClients()?

--Server script

rs = game:GetService("ReplicatedStorage")
admins = {"LawlR", "gungirl60"}
game.Players.PlayerAdded:Connect(function(plr)
	for _,a in pairs(admins) do
		if plr.Name == a then
			rs:FindFirstChild("adminjoined"):FireAllClients()
		end
	end
end)

--Local script, ignore all of the function..

text1 = script.Parent.Parent.t1
text2 = script.Parent.Parent.t2
text3 = script.Parent.Parent.t3
text4 = script.Parent.Parent.t4
text5 = script.Parent.Parent.t5
text6 = script.Parent.Parent.t6
text7 = script.Parent.Parent.t7
rs = game:GetService("ReplicatedStorage")


function adminjoined()
	script.Parent.Parent.Parent.Enabled = true
	repeat wait (.02) text1.TextTransparency = text1.TextTransparency + .03 until text1.TextTransparency >= 1
	repeat wait (.02) text2.TextTransparency = text2.TextTransparency + .03 until text2.TextTransparency >= 1
	repeat wait (.02) text3.TextTransparency = text3.TextTransparency + .03 until text3.TextTransparency >= 1
	repeat wait (.02) text4.TextTransparency = text4.TextTransparency + .03 until text4.TextTransparency >= 1
	repeat wait (.02) text5.TextTransparency = text5.TextTransparency + .03 until text5.TextTransparency >= 1
	repeat wait (.02) text6.TextTransparency = text6.TextTransparency + .03 until text6.TextTransparency >= 1
	repeat wait (.02) text7.TextTransparency = text7.TextTransparency + .03 until text7.TextTransparency >= 1
	repeat wait (.02) text7.Parent.BackgroundTransparency = text7.Parent.BackgroundTransparency + .03 until text7.Parent.BackgroundTransparency >= 1
	script.Parent.Parent.Parent.Enabled = false
	text1.TextTransparency = 0
	text2.TextTransparency = 0
	text3.TextTransparency = 0
	text4.TextTransparency = 0
	text5.TextTransparency = 0
	text6.TextTransparency = 0
	text7.TextTransparency = 0
end

event = rs:WaitForChild("adminjoined")
event.OnClientEvent:Connect(adminjoined)

How do I get the player's name that just joined? I would like to change the text to "(player that just joined) had joined" or something along those lines, but I'm not sure how to get the name.

I am not sure what you mean. I will just give you 2 examples which may be what you want:

local plr = game.Players.LocalPlayer
print(plr.. "has joined the game.")

or

game.Players.PlayerAdded:Connect(function(plr)
	print(plr.." has joined the game."
end

If you wanna do this in client you may want to use the first examples.