Exactly. The Tetragrammaton was God's old covenant name, identifying himself as the God of his covenant people, the Jews.
But when that old arrangement ended and all humans regardless of race, both Jews and Gentiles, could have a personal relationship with God as their father, God saw fit to allow his old testament name identifying himself as the God of the Jews to disappear!
That's why Paul in his famous sermon at the Areopagus never referred to this one universal God as YHWH at Acts 17(nor in fact in any other place in his epistles). God was no longer to be identified as a Jewish God by a Jewish name anymore.
The Watchtower religion, which is basically a quasi-Judeo cult, starkly misses this point, choosing instead to continually hark back to the OT on everything.