2D label on objects in 3D (LWJGL)

In the end I want to be able to create labels like the player names in the below image,

however, I want them to remain the same size no matter how far away or close up the camera is. My first thought is that the labels would have to be rendered orthographically, but then how can I tell where to render them (in order to be above their player)? I figured maybe some kind of backwards ray-tracing, but I’m not sure how this could be done, let alone if this is even the answer.

My question is how can I render labels orthographically over objects rendered with perspective?