Throughout Deuteronomy, the central sanctuary is referred to as the “place which the LORD God will cause his name to dwell” (KJV). The Hebrew word translated as “cause to dwell” is the piel of shachan.
In other parts of the Torah, the qal of shachan is used to refer to God dwelling in the earthly sanctuary. Here are the passages, in the NRSV, with the translation of shachan in bold-face:
Exodus 25:8: And have them make me a sanctuary, so that I may dwell among them.
Exodus 29:45-46: I will dwell among the Israelites, and I will be their God. And they shall know that I am the LORD their God, who brought them out of the land of Egypt that I might dwell among them; I am the LORD their God.
Numbers 5:3: you shall put out both male and female, putting them outside the camp; they must not defile their camp, where I dwell among them.
Numbers 35:34: You shall not defile the land in which you live, in which I also dwell; for I the LORD dwell among the Israelites.
Outside of the Torah:
1 Kings 6:13: I will dwell among the children of Israel, and will not forsake my people Israel.”
Psalm 74:2: Remember your congregation, which you acquired long ago, which you redeemed to be the tribe of your heritage. Remember Mount Zion, where you came to dwell.
Isaiah 8:18: See, I and the children whom the LORD has given me are signs and portents in Israel from the LORD of hosts, who dwells on Mount Zion.
Ezekiel 43:7: He said to me: Mortal, this is the place of my throne and the place for the soles of my feet, where I will reside among the people of Israel forever. The house of Israel shall no more defile my holy name, neither they nor their kings, by their whoring, and by the corpses of their kings at their death.
Ezekiel 43:9: Now let them put away their idolatry and the corpses of their kings far from me, and I will reside among them forever.
Joel 3:17: So you shall know that I, the LORD your God, dwell in Zion, my holy mountain. And Jerusalem shall be holy, and strangers shall never again pass through it.
Joel 3:21 I will avenge their blood, and I will not clear the guilty, for the LORD dwells in Zion.
Zechariah 2:10-11: Sing and rejoice, O daughter Zion! For lo, I will come and dwell in your midst, says the LORD. Many nations shall join themselves to the LORD on that day, and shall be my people; and I will dwell in your midst. And you shall know that the LORD of hosts has sent me to you.
Zechariah 8:3: Thus says the LORD: I will return to Zion, and will dwell in the midst of Jerusalem; Jerusalem shall be called the faithful city, and the mountain of the LORD of hosts shall be called the holy mountain.
We see the view that God dwells (shachan) in the midst of Israel in the tabernacle or the temple on Zion. I think that the Deuteronomist responds to this view with another use of shachan–the piel–to say that God doesn’t dwell in his sanctuary, but he causes his name to dwell there. Something else of significance: Exodus-Numbers often use the term mishkan (tabernacle), which has the root of shachan. But Deuteronomy doesn’t use that term. Could this be because it carries the association of God dwelling in a sanctuary, a concept that Deuteronomy disputes?
Another issue I’ve wondered about: Does shachan mean to permanently dwell in a place, or can it mean “to visit”? If it’s the latter, then God can live in heaven and only visit the Tabernacle on certain occasions. It turns out that the word can mean the latter. Exodus 24:16 uses the word for God’s glory abiding on Sinai for a set period of time. Exodus 40:35 has the same thing with the Tabernacle: God’s cloud comes and fills it at its dedication, but it’s not always there. But shachan often means living in a tent, or in a region. Since the Tabernacle is God’s tent, I think many of the shachan passages mean God is living in Israel’s midst. Plus, I Kings 8:27 (Dtr) goes out of its way to dispute that God dwells on the earth. It uses yeshev rather than shachan, but it’s still disputing that idea.
See 7931 for all the uses of shachan.