Peace of Christ (15): Paul here continues the topic of Christian harmony. The way we treat others is to reflect the peace we have from Christ. Our inner peace is what makes us maintain peace with others. God placed every believer into a church for this very purpose ("to which you were called in one body"): that we would give to others what we received from the Lord. And we do this with an attitude of gratitude. We are a thankful people of peace-makers.
Word of Christ (16): We are also to let the word of Christ dwell in our church richly (not sparingly!). The word of Christ is the truth about and from Christ. We reinforce this message ("teach"), and we admonish one another against sin with this message. Paul highlights one specific way to accomplish this: singing (Eph. 5:19). Now, singing could degenerate into a meaningless habit. Thus, we are to sing "with thankfulness" and with sincerity ("in your hearts") to God.
Name of the Lord (17): Then lastly, before addressing the specific groups in the church (3:18ff.), Paul adds a comprehensive command to "do all" things in line with the character and authority of the Lord Jesus. He should be manifest in everything we do. And we do all this with thankfulness. We keep coming to God through Christ (Heb. 10:19-22) with expressions of thanks (1 Thes. 5:18).
 3:15 actually starts with "And [kai (καί)]" (ESV, NKJV). Harmony (3:12-14) is still the focus in these verses.
 Every believer understands this peace. It is the peace with God that he has through Jesus (1:20; Rom. 5:1).
 As we received forgiveness from the Lord, we extend it to others (3:13). So we do with peace. Cf. Phil. 2:1-2.
 "Be thankful" is a stative, describing a state of being. We have a thankful attitude as a people blessed of God.
 "Richly dwell within you [plural]." The one-anothers here show that the focus is on the church community.
 This is both the message about Christ (1:28; 1 Cor. 2:2) and the message from Christ (1 John 1:5; John 8:31).
 In Scripture, "in the name" refers to an action done in concert with the character of the person in question (cf. Matt. 10:41). "In the name of the Lord" specifically appeals to the Lord's authority (cf. 1 Cor. 5:4).