While it's true God had various names in the Hebrew Bible, the name YHWH has a distinct claim. As Philo says, it was the name of God written on the headband of the high priest. The fact that it became set apart as the unpronounceable name of God among Jews shows that it was considered unique.
The earliest copies of the LXX used various forms of YHWH or the Greek transliteration IAW. (There are about 7 such examples) None of the Jewish fragments that survive show KYRIOS instead of the divine name. The earliest Christian copies using KYRIOS date no earlier than late second century AD. The fragment of Genesis that leaves spaces for either YHWH or KYRIOS is quite late, from the third century, and probably Christian. It is probably indicative of the transition from using YHWH to KYRIOS in Christian practice.