Now that Excel has FINALLY regained her memories and gone back to her original personality, I think I'm finally okay to essay about the whole Teriha thing. Also it's the easiest of many, many essays I want to write right now.
Basically, the Teriha thing goes like this: Excel and Elgala are stuck on an island, as happens sometimes when antics go awry. Il Palazzo shows up to pick them up, most likely because he is tired of having to make new cardboard stand-ins after he drops them into the pit. As he is teleporting them out, he gets distracted and leaves Excel behind. (I should probably note here that canon sort of leaves it up in the air whether he's distracted or whether he ditches her purposely. This should and probably will be an essay on its own since it has nothing to do with Excel's amnesia and everything to do with Il Palazzo's characterization, but suffice it to say, I believe he dropped her out of senility, not malice.)
Anyway, after Il Palazzo leaves her behind, Excel is stalked by this really badass priest guy trying to convert her to Christianity. They go on a hilariously epic chase all around the world, which ends with her falling into the river. She almost dies, but is instead saved by Shiouji's cousin Umi, who takes her home and nurses her back to health. At this point, she has total amnesia and Shiouji's mom gives her a new name: Teriha Shiouji. Meanwhile, Il Palazzo whips up a new Excel and actually begins successfully conquering things (via capitalism, of all things).
For a whole year in canon (and more than that in real time :/) Teriha is a vastly different person than the Excel we know and love. She's quiet and shy and afraid of basically everything. At first she wants nothing more in life than to watch TV all day and hide from the real world, but she eventually feels guilty for imposing on the Shioujis and ends up getting a job. Her memories return slowly, but here's the thing - she doesn't want them to. As Teriha, she wants to stay Teriha. This is because when she does remember, she only seems to remember things like that time she had to run through a mine field, and she's terrified of who she used to be. (I guess to be fair, her life in ACROSS was kinda 99% terrible shit happening to her.)
I can't really go too much into the details because everything after that point hasn't been translated yet (only in bits and pieces by Kohaku, whom I love with my feelings), but as soon as she sees Il Palazzo again, everything changes. Her obsession starts coming back and she eventually decides that she doesn't belong with the Shiouji family. I can't find the exact translation because I'm not the kind of person who believes in organizing the things she saves, but Teriha basically says, "I should really just get a boyfriend and watch Umi and Shiouji get married and live a normal life... but every time I think about Il Palazzo, my heart burns, and I know I'm really just waiting around." When she and Il Palazzo finally do come face to face, she remembers herself, forgets her time as Teriha, and all is well. Except that it isn't because Il Palazzo is still in evil mode, but once again, that's a different essay.
Characterization-wise, her time as Teriha only affects her in small ways (and because of this, I fully intend to goad the Excel Saga cast into updating sooner or later). One she's back to normal, she uses "Teriha Shiouji" as a fake name, and even if she doesn't strictly remember Umi, she sorta-kinda recognizes her and various other Shiouji-related things. Also, throughout the series, Excel's stress levels are ratcheted up and up until she's basically 8| all the time (note to self: essay on this too), and her year-long vacation from ACROSS seems to help calm her down a little.
Plot-wise, I think she just needed to be out of the picture so ACROSS could actually succeed for awhile, hahaha.
The fandom theory shared by almost everyone (including the English-language editor of the manga) is that Teriha is Excel's "real" personality; ie, the personality she had before she joined ACROSS. And it is a theory that makes sense. Deep beneath all of the antics, retardation, and universal miasma of unresolved sexual tension, Excel Saga a mystery series where you're trying to figure out three things: What happened to Shiouji's parents, what the fuck is Solaria actually supposed to be, and Excel and Il Palazzo's true identities. So do I think that Teriha is the "real" Excel, that hidden second self that's been hinted to exist from the very beginning?
No fucking way.
Remember the time that Garfield lost his memory and became the kind of cat that chased mice? Personality-reversing amnesia is a freaking Saturday morning cartoon convention. Or for maybe a better example, that one time that Rikdo gave his own little twist to the "mistaken doctor's report makes everybody think their friend is dying" plot. It is going way out of its way to be epic now (and succeeding, mind you), but this is still Excel Saga. It is still a very silly manga, and Teriha's emo is very tongue-in-cheek.
Besides that, this isn't the first time Excel has gotten amnesia. It's implied like a brick that even she doesn't know who she was before she joined ACROSS, and when she gets amnesia in volume 4, her personality remains exactly the same. It seems a lot more likely to me that besides the physical shock of nearly dying, she honestly just had a nervous breakdown, not reverted to some underlying personality. Don't get me wrong, she definitely has an underlying personality, but everything up til now has indicated that said personality is "geeky science major," not "Miss Saddy McEmo Waifface." I think this is a red herring. A red herring that lasted for like four volumes because Rikdo sucks balls at pacing.
Trying to compare Teriha and Excel is a waste of time, because the real comparison is between Excel and Ropponmatsu. It's not entirely clear which is the copy of the other, but that's not really important. What is important is that whatever the hell Excel and Ropponmatsu are supposed to be (maybe keys to the weapon that can destroy the world, maybe the actual weapon that did destroy the world, very probably the former ruler of the world), it's important. Saying Teriha is Excel's original personality is like saying that Ropponmatsu I is Ropponmatsu II's original personality. I don't think it actually works that way.
And you know what? Even if Teriha was Excel's default Rei Ayanami personality while Il Palazzo was CREATING HER in a TUBE (note: previous statement is not strictly canon... yet), that doesn't make it her "real" personality. If Il Palazzo created the strong, smart, fuckin' awesome Excel, good for him. PROPS TO IL PALAZZO.
In conclusion, I am a lot more okay with this plot point now that the end is in sight, even if it isn't going to be in English for like 139012830 years. Also, I do intend to update Excel one of these days, I am going to acknowledge her year as a Shiouji, and I will be bringing back the Hippo of Traumatic Amnesia every goddamn chance I have.