I have the Infinity enchantment on my bow, so I only have to have 1 arrow in my inventory.
I renamed this arrow so that it wouldn't stack with the arrows collected from killed skeletons.
But if this arrow is shot by a normal (unenchanted) bow, the arrow is picked up as a normal arrow instead of the renamed one.

How to reproduce:

• Get 1 unenchanted bow, 1 bow with the Infinity enchantment, 1 renamed arrow and maybe some extra arrows to see that it stacks up.

• Shoot the renamed arrow with the Infinity bow.
  As expected you will still have the renamed arrow in your inventory

• Shoot the renamed arrow with the unenchanted bow
  The renamed arrow disappeared from your inventory

• Retrieve the renamed arrow
  You can see that it has changed back to a normal arrow and it stacks up with the rest of the arrows