And it came to pass after I, Nephi, having heard all the words of my father, concerning the things which he saw in a vision, and also the things which he spake by the power of the Holy Ghost, which power he received by faith on the Son of God—and the Son of God was the Messiah who should come—I, Nephi, was desirous also that I might see, and hear, and know of these things, by the power of the Holy Ghost, which is the gift of God unto all those who diligently seek him, as well in times of old as in the time that he should manifest himself unto the children of men. 1 Nephi 10:17
The term "Holy Ghost" appears 87 times in the Book of Mormon and here in 1 Nephi written 600 BC.
The term "Holy Ghost" appears 0 times in the Old Testament and 89 times in the New Testament. It's a New Testament phrase about an Old Testament concept.
In the Old Testament, the Holy Spirit was known as "the Spirit" or "the Spirit of God." Joseph Smith weaved 1800s terminology into these "ancient" documents.