For example, the Byzantine Empire called itself "Rome" and was likewise called "Rome" by her neighbors. "Ptolemaic Egypt" is another modern name, it's inhabitants simply referred to themselves "Egypt" (I think)
But what did the Seleucids call themselves? And what did her neighbors call her?
Hey, a question almost directly related to my research!
So, the problem we have with the Seleucid Empire is the immense dearth of primary sources composed by the Seleucids themselves. With the Byzantines, we have a large number of writers whose works and letters still survive. In Egypt, we have a great deal of papyri that include royal, administrative, and personal correspondance that provide nice insights into the running of the Ptolemaic Empire (although I doubt they called themselves "Egypt" in their own writings, I cannot say for certain; I believe Roman historians are the authors who called them "Egypt").
As for the Seleucids, however, we do not have many primary sources that are from within the Seleucid Empire, and were written by Seleucid administrators or royal scholars. What we do have are a number of administrative documents written by more local government officials: ration lists by priests in Babylon; land deeds written by officials in Syria; temple dedications written by priests in eastern Asia Minor. We do not have narrative histories by scholars from within the Seleucid Empire, akin to those written by later Byzantine scholars.
In the documents that I study, which are administrative and legal documents from Seleucid Babylonia, local officials refer to the Kings by name whenever they refer to the royal administration. "In the reign of King Seleucus/Antiochus/Demetrios/etc." is what is used. The words "Seleucid Empire" is not present in this corpus.
Now, it is possible that Seleucid historians did refer to their own state in some way, but these histories are unfortunately lost. Historians like Megasthenes, Patroclus, and Berossus wrote histories under the patronage of the Seleucid kings, but their subjects were the histories of various lands within the Seleucid Empire. Megasthenes, for instance, wrote a history of India, while Berossus wrote about the ancient history of Babylon. We know this much because of some quotations and discussions we find in the works of later scholars (like Eusebius), but the quotations are small and sparse.
Nonetheless, we do not have a history of the Seleucid Empire written by a Seleucid historian. As a result, we do not have any name that the officials of the Seleucid Empire would have called their government. "King Seleucus" and the ilk are about as close as we can get.
Check out Paul Kosmin's latest book, The Land of the Elephant Kings: Space, Territory, and Ideology in the Seleucid Empire, for the latest research on this topic.