Badges update automatically and link to the mod page on MineUniverse.
Player heads keep their custom names and lore tags after being placed down and picked up again.
This is an unofficial fix for MC-174496, which was finally fixed in 1.20.5!
Note:
If you still want lore and other custom data to be kept in 1.21+, check out the datapack continuation of this mod, Keep Head Data.