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A very long time ago, the Church decided that it was important for people to hear the gospel in their own language. That's at the core of why the New Testament was written in Greek and not in Hebrew. The earliest churches used the common languages of the day. The Roman Catholic church picked up Latin along the way and it's still their official language. For several reasons, the church didn't really keep up with the tradition and held on to the Latin mass well into the 20th century. Martin Luther picked up the tradition again by translating the Bible into German. He was then followed by several translators over the centuries who translated the Bible into their native languages. That tradition continues today with Bible translators who work to give small tribes Bibles in their own languages.
Translators try to be as accurate as possible but conveying the meaning takes priority over literal word for word translations so little nuances like that sometimes get lost. English speaking Christians sometimes use the different names of God in Hebrew and in English for worship and prayer. They're just not usually in the translation of the Bible we use.
Upvote:5
To be clear, Christians do use other names of God in some contexts.
Michael Card's song El Shaddai was wildly popular in the 80's, and is often credited with launching the career of Amy Grant.
I remember singing Jehovah Jireh, and dozens of other songs like that.
Kay Arthur has a popular study based on the names of God, directed especially at women.
That list came to mind in the first 30 seconds of thinking. There are many, many others.
As to why these aren't more popular? I'd suggest it's simply linguistic. People gravitate towards the familiar when addressing a person. Even if the Duke of Cambridge has 4 main names and 21 titles, they're still going to call him "Prince William" ninety nine times out of a hundred. It's the same with "God." Hebrew is hard to pronounce, has the appearance of being overly formal in the King James, and generally is more foreign to the culture of mainstream American evangelicalism than anything else. In spite of that, as shown above, we often incorporate it. As such, I think the question should actually be reversed - why use the Hebrew as much as we do?