Nametags are only applied client-side if the Ghast has its eye-level blocked by slabs.

A nametag item is removed from the inventory and the name is displayed above the ghast, however it will still despawn if the player moves far enough, and if the stack of nametags is moved it will go back to the number of nametags the player had before renaming the ghast.

If the slabs at eye-level are removed the renaming works normally, correctly removing the item and applying the namechange.

In the attached screenshot, a setup to reproduce the bug is shown. If the ghast is renamed while in the slabbed area, it's only client-side. If it's renamed in the part without slabs everything is normal.