I don’t think we can determine from history one way or another about the intention of God regarding his name because it’s all open to interpretation. Say we focus on the disuse of God’s name in the Christian Era, we can either conclude that was God’s will that people no longer use the name, or else we can say that was Satan trying to hide the name of God. Point out that Jehovah’s Witnesses revived use of the name in the 20th century and you can say they were 1) going against the will of God 2) other churches use the name as well so JWs are not actually that distinctive, or 3) Jehovah purposely used JWs as the means to revive awareness about his name. You could make coherent arguments for any of those perspectives, it seems to me. The facts of history alone don’t provide one overwhelming interpretation.
What I am pretty convinced about is the fact that Jesus and the early Christians probably did use God’s name regularly and that this has been obscured by later Christian tradition. I don’t think it’s a coincidence, for example, that Jesus’ name includes the divine name, and the meaning of Jesus’ name is highlighted in Matt 1:21. I don’t think it’s a coincidence either that Jesus three times answers Satan using quotations containing the divine name (Matt 4 and Luke 4). All the earliest LXX contain forms of the divine name. Christian names lists contained the divine name in the form Yaho for centuries. Plus Leviticus fragment used Yaho, and Roman authors say that Jews called their God Yaho in the first century. This means the earliest Christians understood and used the divine name in the form Yaho - I don’t see what other reasonable conclusion can be drawn.