Solution 1:

Edit : Feature implemented in 1.05

VintageTribe (Quality Assurance Tester on CDProject team) wrote about it this week :

Hey all,

this feature is actually being implemented and will be available soon in one of the upcoming patches.

Happy hunting, witchers!

(source : http://forums.cdprojektred.com/threads/37681-How-to-turn-off-name-tags-in-the-witcher-3-%28animals-etc%29?p=1698014&viewfull=1#post1698014)

Solution 2:

While 1.05 did fix the NPC labels, the "Talk" icons remain. Here's a mod that claims to remove them though in case anyone finds them as immersion breaking as I do: http://www.nexusmods.com/witcher3/mods/339/ (I haven't tried it yet though)