Vanilla Chest Behavior is that when you rename a chest or trapped chest, the name of the chest is displayed in the inventory. The Warded Chest doesn't do this. Since it looks like it was never designed to, I guess this is technically a feature request? At least, according to Mojang's trackers it would be. It's also far from the only Chest in modded Minecraft that doesn't- even Hungry Chests don't respect this.

It should be easy enough for me to add this. But if you're wondering, it isn't a "built-in" behavior for inventories, which probably explains why I and a lot of other mods missed it.