How do I identify a certain player by using a global script?

You can have a local script make the value of an object value the player

Local Script

--assuming the local script is in starterpack and the objectvalue is under the name of "player" in the workspace

workspace.player.Value = game.Players.LocalPlayer
script:Destroy()

Server Script

--workspace.player.Changed:connect(function(value)
player = value
end
--now you can reference the player using player.

Alternatively, you could have a table that is changed whenever a player joins or leaves.

Server Script

local players = {}
game.Players.PlayerAdded:connect(function(player)
players[player.Name] = player
end)

game.Players.PlayerRemoving:connect(function(player)
players[player.Name] = nil
end)