When creating a scoreboard objective with the criteria type "stat.useItem.minecraft.name_tag" the scoreboard fails to increase a player's score for that objective when renaming a mob using a name tag.

To recreate:
Type the following commands into chat
/scoreboard objectives add nametag stat.useItem.minecraft.name_tag
/scoreboard objectives setdisplay sidebar nametag

Then, use a nametag to rename a mob. You will notice the sidebar will not change.