Under most circumstances, throwing a snowball/ender pearl/egg/what-have-you copies the item's NBT data (name, lore, custom model data). However, if the item being thrown is the last in the stack, then it just throws a regular projectile.
Steps to Reproduce
Grab yourself a single snowball and rename it.
Toss it out.
Run the command "/data get entity @e[type=snowball,sort=nearest,limit=1] Item"
Behold the given error message.
Now, repeat the process with two or more snowballs. Throw exactly one snowball, and repeat the command. Behold the snowball's delicious item data.
This is still in release 1.14.3. Testing various projectiles shows that it affects Snowballs, Eggs, Bottles 'o Enchanting, and Ender Pearls. It does not affect Eyes of Ender or Splash Potions. I've attached a video showing this (using the CustomModelData tag) in 1.14.3 with various items.
Still in 19w14a