Minecraft – Putting tags above blocks when looked at

There's a built-in way to do this (that has built-in balancing drawbacks) and a modding way.

To hide your name from other players, just sneak (crouch) the whole time you are trying to avoid detection. Your name won't show through blocks then, and even without blocks in the way it will be dimmed and harder to read.

The modding way is a Bukkit plugin called HeroSneak that will add a server command /sneak (along with persmissions hooks for who can use it, etc., so as usual you will need other mods if you want to restrict it). HeroSneak exploits the built-in way of hiding your name: it just activates the name-hiding feature with a command instead of tying it to whether or not you are crouching.

in versions before 1.8.3 I know that you could make armourstands with custom playerheads just larger than a block. in the newest versions, howerver, custom playerheads do not work, I wouldnt use new versions for command blocks for several other reasons, too, such as rendomized dispensers.