Can we make any inference back to a change in the nature
of Eva-06 based on the fact that the nature of the lance it 'owns'
has changed? Is it too much of a stretch to say "the lance changed, therefore the Eva changed"? Perhaps that is what Kaworu spends so much time pondering. Perhaps the lance change is a giveaway that Eva-06 is infected and that releasing it is a very bad idea. (I'm still really intrigued by the fact that Rei was apparently under orders
to behead the Eva and release the Angel trapped within.)
Well, u actually make an interesting point that's directly connected to the religious figure of Longinus.
Longinus and Cassius are essentially the same person (wikipedia...), Cassius was its "name" before he converted to christianity. After that his name was changed to Longinus.
So yeah, i guess that Cassius spear may have indeed transformed into Longinus spear with the time. Just like Cassius "changed" name to Longinus after changing his "nature".
Cassius himself converted to christianity after piercing Jesus with his spear (changing his name afterwards). It's not surprising then that, when a Cassius spear pierces an evangelion (a godly being of some kind/an Adam related being i guess), it eventually turns into a Longinus spear.
Maybe it's alrdy been pointed out somewhere else in the thread too.
As for spear themselves, i doubt they say anything about the name of the owner.
EDIT: We could even see things like this: 4 spears, 4 adams. All of them start out with a Cassius type. After each impact one Cassius spear turns into a Longinus spear. We've had 3 impacts (if we consider the one in 3.0 as a continuation of the one in 2.0) and probably 3 Longinus spears (1 missing), the spear that's left may still be a Cassius type.
So any idea what the role of the spears are? We've gotten an idea of their capabilities, but so far it isn't clear whether or not they were meant as fail-safes against the Adams like in NGE, or if they were more of an instrument for them. Kaworu was intent on using them as tools for personal use; but I wonder if that's just due to education he picked up from being a lackey for SEELE, or demigod-privileged knowledge.
My guess is that Cassius spears serve as a failsafe, to keep Adams under control(?). Prolonged contact with Adams (or similar beings) eventually turns them into Longinus spears, at which point they may lose their sealing capabilities once they're removed from the Adams. Let's say that Cassius spears are the only ones that can stop an impact and that only one is left. If they use the one that's left (provided someone has found it), it's going to turn into a Longinus type eventually. That would make one more impact after the fourth completely unstoppable (unless Shinji pulls off something...)
With all this in mind it's not so weird that the use of 1 Longinus and 1 Cassius may redo the world. The Cassius represents the previous state of the Longinus spear, contact between them may allow to go back to a previous state of existence (it makes sense only on a symbolical level, but still...)