Like if someone was standing in front of a wall, you can see their name. But if they were behind the wall, you couldn't.
The NameOcclusion Property is exactly what you are looking for.
In a LocalScript in the StarterGui:
local plr = Game.Players.LocalPlayer (plr.Character or plr.CharacterAdded:wait()):WaitForChild("Humanoid").NameOcclusion = Enum.NameOcclusion.OccludeAll
Adark is right, but his code results in an error. Do this instead:
from a server script in workspace
game.Players.PlayerAdded:connect(function(plr) (plr.Character or plr.CharacterAdded:wait() ):WaitForChild("Humanoid").NameOcclusion = Enum.NameOcclusion.OccludeAll end)