When you switch into the front facing 3rd Person view (accessed by pressing F5 twice), the pitch of other players' name tags will be placed relative to the camera still being behind the player. That means that if you look up or down, the name tag appears tilted when it should appear flush with the screen.
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Duplicate of MC-5404- If you have not, please use the search function in the future, to see if your bug has already been submitted. If you could not find the original report, please comment with the keywords you searched for.
I have tested this in vanilla minecraft without texture packs using the default launcher in both 1.6.2 and 13w37a. This is not a 3rd party issue. Please reconsider the status change and test it first.