What does "shem" mean in Tanakh?
"The effect that a name produces rests on the power possessed by the person who bears this name. The result is the usage of shem in a dynamic sense as the sum of a person’s deeds and accomplishments, means and reputation. As a representative of the personality, shem consequently signifies dynamically not just descendants but also (as in some modern languages) fame, honor, reputation, so that shem often alternates with terms like tehilla (fame, praise) tipheret (splendor, distinction). An (honored) name (shem) is more precious than great wealth (Prov 22:1) and better that fine ointment (Eccl 7:1). In contrast, insignificant and contemptible persons are nameless (Job 30:8).
Because shem in the dynamic sense signifies a person’s vital, material (means, property), and spiritual (fame, honor) aspects, the name can also survive one’s death; hence one is concerned for one’s name. Because Absalom had no son to herald his name after his death, he erected a memorial stone while still alive (2 Sam 18:18). God promises the eunuchs a memorial (yad v’shem) in the temple precincts (Isa 56:5) through which they will remain in the memory of God’s community.
--Adapted from A. S. van der Woude, Theological Lexicon of the Old Testament (TLOT)
(16) The word of the LORD came to me: (17) O mortal, when the House of Israel dwelt on their own soil, they defiled it with their ways and their deeds; their ways were in My sight like the uncleanness of a menstruous woman. (18) So I poured out My wrath on them for the blood which they shed upon their land, and for the fetishes with which they defiled it. (19) I scattered them among the nations, and they were dispersed through the countries: I punished them in accordance with their ways and their deeds. (20) But when they came to those nations, they caused My holy name to be profaned, in that it was said of them, “These are the people of the LORD, yet they had to leave His land.” (21) Therefore I am concerned for My holy name, which the House of Israel have caused to be profaned among the nations to which they have come. (22) Say to the House of Israel: Thus said the Lord GOD: Not for your sake will I act, O House of Israel, but for My holy name, which you have caused to be profaned among the nations to which you have come. (23) I will sanctify My great name which has been profaned among the nations—among whom you have caused it to be profaned. And the nations shall know that I am the LORD—declares the Lord GOD—when I manifest My holiness before their eyes through you. (24) I will take you from among the nations and gather you from all the countries, and I will bring you back to your own land.
In this context, what does profanation of the divine name mean? How has G-d's name been profaned? What is the opposite of "profanation" in this text?
Alternate translation: “Instruct Aaron and his sons to be scrupulous about the sacred donations of the Israelite people; they should not desecrate My holy name which they sanctify for me, I am YHWH.”