Server to All Clients

Scripts

ServerScriptService

local ReplicatedStorage = game:GetService("ReplicatedStorage")
local Players = game:GetService("Players")
 
local remoteEvent = ReplicatedStorage:WaitForChild("RemoteEvent")

Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function(character)
        character:WaitForChild("Humanoid").Died:Connect(function()
            remoteEvent:FireAllClients(player, player.Name)
        end)
    end)
end)

Part

local trapPart = script.Parent
local function onPartTouch(otherPart)
    local partParent = otherPart.Parent
    local humanoid = partParent:FindFirstChildWhichIsA("Humanoid")
    if ( humanoid ) then
        humanoid.Health = 0
    end
end
trapPart.Touched:Connect(onPartTouch)

LocalScript under TextLabel

local label = script.Parent
label.Visible = false

local ReplicatedStorage = game:GetService("ReplicatedStorage")

local remoteEvent = ReplicatedStorage:WaitForChild("RemoteEvent")

local function onNotifyPlayer(name)
   label.Visible = true
  label.Text = tostring(name) .. ' Died'
  wait(5)
  label.Visible = false
end
 
remoteEvent.OnClientEvent:Connect(onNotifyPlayer)