It was John's Book of Revelation that led later writers to associate the word "Babylon" with "the city of seven hills", and that didn't begin to circulate until 100 AD.
Peter was writing to Jews in 67 AD, and the Jews knew where Babylon was --- it was on the Euphrates.
Wait, wait! Assuming what is to be proved! I don't know that you're wrong, but I don't know that you're right either. I wouldn't make a big deal of this but it struck me that the notes in my NEB blithely assert that Peter is writing to Gentile Xtians, while my NAB -- the translation evidently done as a project by an English as a Second Language class -- In the Study bible version, (No pictures, though, darn it!) says,
Numerous allusions in the letter suggest that the churches addressed were largely of Gentile composition (1,14,18; 2,9-10;4,3-4), though considerable use is made of the Old Testament (1,24; 2,6-7.9-10.22;3, 10-12)I don't know why they punctuated the references that way. I just pray, pay, and obey. And I'm not saying they're necessarily right. I'm just saying it's not a slam-dunk that this was addressed to Jews.
Circulate? When was it written? How do you know that Revelation is the first instance of this code name? And how do you know that Peter didn't already use it? Christians were largely underground at the time; they would have needed to misdirect any Roman inquisitors away from overt criticism of the Empire.