When right clicking a saddled pig with a name tag it does not name the pig. You'll either start riding the pig, or move slightly when shift right-clicking.
This relates to MC-14525 , that fixed this issue for adult villagers etc., but not for saddled pigs. Also relates to MC-2188 and MC-19033 .
This bug appears to be back again, if you hold the name tag in your off-hand. The name tag does work in the off-hand, but not for saddled pigs (maybe same also counts for villagers, not tested) in minecraft 1.12.1. I took the name tag off and put it in my main hand, and then it did work.
I assume the fix for naming saddled pigs (and villagers?) might internally only function on the main hand.
Also, when I tested the renaming the saddled pig, I was holding just an axe in the main hand, or another random item, which seemed not to affect the thing in any way.
MC-106302
This bug appears to be back again, if you hold the name tag in your off-hand.
The name tag does work in the off-hand, but not for saddled pigs (maybe same also counts for villagers, not tested) in minecraft 1.12.1. I took the name tag off and put it in my main hand, and then it did work.