Breaking a named Sack causes it to lose its name.

How to replicate:
Use anvil to rename Sack
Place down the named Sack
Break the Sack until its broken
Pick the Sack up

Just to add to this, over half a year later, it "only" happens when you break an empty sack, that the name disappears. If you give the sack a name while it has items in it and always makes sure there are items in it when it is picked up, then it doesn't happen.
It's like it resets its metadata when empty and broken.

EDIT: Got to thinking, maybe it's related to why the sacks doesn't have a generated inventory until they've been put down? As in, you can't put anything into them until they've been "initialized", it's as if they're not registered until first use.