The wording of the verses (above) from Malachi, tell us whose names will be written in the book of Remembrance. In contrasted with those who are the subjects elsewhere in the book of Malachi, which is written to Israel.
We read
in Exodus 28:15-30 of the breastplate worn by the High Priest when he went in before the Lord: made to God's pattern and design; made out of woven fine twined linen, in gold, blue, purple and scarlet, folded in two to form a pocket, which was square, and a span in width and height; on it were placed in four rows, jewels set in gold enclosures.
The 1st - a sardius, a topaz and a carbuncle,
The 2nd - an emerald, a sapphire and a diamond.
The 3rd - a ligure, an agate, and an amethyst,
The 4th - a beryl, an onyx and a jasper.
On each stone was engraved, like a signet, THE NAME OF A TRIBE OF ISRAEL. So when the High Priest went unto the holy place,
they were there upon his heart (v.29)
before the Lord continually as a memorial before Him. The breastplate also contained the Urim and Thummim , and was used as a means whereby God made known His will, to the High Priest on Israel’s behalf
'For the LORD hath chosen Jacob unto Himself,
and Israel for His peculiar treasure.'
(Psa 135:4)
'My Jewels' - His precious possession/a peculiar treasure.