Can less knowledgeable, not-quite-yet-Orthodox (at least not for another 21 days...but who is counting) answer? Because these are really just language questions.
I'd appreciate some clarification as to the evolution of the Christians' name that rejected the Council of Chalcedon in 451. To my understanding, for 1500 years or so, they were known as Monophysites because of their belief in the one nature. Then, for "PC" reasons, they were called Non-Chalcedonians. (This is an important change between the first and second editions The Orthodox Church.) At a later time, this group was then referred to as "Oriental Orthodox".
As they always rejected the heretical monophystism of Eutyches, it was never appropriate to call them "Monophysites", no matter how popular it has been in the past. (See "Coptic Interpretations of the Fourth Ecumenical Council" by Fr. Matthias Wahba for more on the Coptic rejection of Monophysitism and of Chalcedon.)
Why Oriental Orthodox? "Oriental" literally means Eastern. Unless "Eastern Orthodox" refers to the Eastern Roman Empire
Well, it does in Arabic, whereby you guys are "Rum Orthodoks". I have seen on occasion a few apologetics texts even in English that ask about differences between the "Roman Orthodox" and the Coptic Orthodox, but of course it is the norm in English to say "Eastern", as those in union with Rome have sort of absconded with that particular adjective (as they have tried to do with the noun "Pope" for centuries now, much to our chagrin
and "Oriental Orthodox" refers to the geographic east. Of course, "Romans" would say that Orthodoxy isn't restricted to the East, so it must refer to the Eastern Roman Empire. Is "Oriental Orthodox" a name bestowed on the Non-Chalcedonians by Western academics, like "Eastern Orthodox" on the Chalcedonians?
Well, we are just Orthodox among ourselves, right? Just like you guys don't shy away from calling yourselves "Catholic" when this indeed your own understanding of your church, and it is obvious what this means (and doesn't mean) to the audience in which you are speaking. So you can see that, for instance, in Coptic the name for our church is just "ti-ekklesia en-remenkimi en-orthodoxos" (remenkimi = Copt = Egyptian). Nothing about "Oriental" or "Eastern" in there. That is a convenience to basically say "not in communion with the Chalcedonians", because it is quicker to say than that whole sentence. (I don't know where it started, though; again, I can only go by Arabic, where Oriental Orthodoxy is quite literally translated "Orthodoksiya mashriqiya"; maybe indicating a borrowing from the West?)
I don't think our churches are too geographically dissimilar, are they? Granted there are some places where for historical reasons most churches are EO (e.g., Greece) or OO (e.g., Ethiopia), but neither would say that this somehow defines their faith, only speaks to their historical circumstances.