New nametags (no previous label) cannot be named in an anvil by clicking in the name field and typing. Instead, we need to get to the field using the TAB key on the keyboard.
If a nametag has previously been given a label, it works fine.
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@Stannya, thanks - just had that pointed out to me as well! I was searching on "nametag", without realising it affected other items in the anvil.
EDIT: Can't see a way to mark it as duplicate myself, a mod may need to do it.
Duplicate of MC-173725