Rare items known as Primordial Souls are "pure essence of Gaia", so the functionality of these items are powerful and greatly benefit the player. They are dormant, but through a certain process, they become Animate. When Animate Souls are used up, some of them may break, others may revert to Primordial state.

Alpha state

The Alpha state allows the player to set a spawn point with an item. Conditions require being in Gaia and on a solid block, and if the block below is no longer solid, the Animate Soul will break and return to Primordial state. When destroyed, spawn is reset to the world, and if a new spawn point is created, the Soul becomes inactive (can be right-clicked to reset it to position, potential waypoint idea).

Beta state

The Beta state allows boss weapons to shape-shift into other types of weapons. These cycle through Melee, Ranged, Shield, repeat. Each Crafting recipe costs 1 durability of the Soul, and once depleted it will disappear. Perhaps have a different method of Crafting, or just keep it as is.

Gamma state

The Gamma state allows for material duplication via a new Tile Entity. These have more durability than Beta state, but will still break once depleted. These are used more as part of the input (but not directly), so their durability is not taken until the process begins.

Delta state

The Delta state is the core of the Honing mechanic. In order for a weapon to be honed, the centre piece of the structure requires a Delta Soul. Unlike Beta and Gamma states, the Soul randomly depletes over usage, and once fully depleted, it reverts to Primordial state. Breaking the structure in some way will not revert it.

Epsilon state

The Epsilon state is the base item required to craft a homing item to structures such as Malachite Watchtowers. Unlike Eyes of Ender, these will not have a chance to break, rather will always drop.

I've decided that instead of Primordial Souls being the main item used to craft all these powerful items, they will instead be another crystal called Celestine.

As for the naming scheme and how to name one, that remains up in the air. It'll be very likely that the proposed naming scheme will be a little different so it can be more open-ended and not a sort of "order", ie. using the Greek Alphabet implies an order.
It would be annoying as is to introduce a new Block Entity for turning Celestine into an "active" state, so it may very well be I cut the middle man out and just name these "states" as the item they are to become. In fact, I will do that right now.

Alpha State - Soul Keeper
Beta State - Recombiner
Gamma State - this will depend on how material duplication will happen, but it will maintain the idea of being a Core/Engine
Delta State - Chakra Nexus
Epsilon State - Synergizer