Taum

Alt+E on a tamed boar or hen and it follows you. Alt+E again and it stays. That is the whole mod.

Why this and not a leash item

The first design was a crafted halter and a lead - an item, a worn model, rope physics. It was cut to this on purpose: the thing the mod exists for is walking one animal to its new pen, and vanilla already contains everything that needs. Wolves and lox follow through the game's own command system; boars and hens have the same machinery and merely lack the flag that lets a player reach it. Taum opens that one gesture, and the game itself does the following, the messages, and the multiplayer ownership.

E still pets. Shift+E still renames - vanilla already owns both, which is why following lives on Alt (configurable).

Works on any tamed creature the game marks non-commandable, so a modded animal gets the same gesture for free.