The name Lutheran usually identifies what a congregation believes, teaches, and confesses. Basic Christian honesty and integrity means that no person or congregation should aim to deceive anyone with this word Lutheran in the identity of the congregation.
So what does this word Lutheran mean?
The standard for explaining the teachings and purposes of a Lutheran congregation can be found in the Book of Concord. In 1580, this book was published to give a true and unadulterated statement of the teachings of the Lutheran church. There are several documents that are included in this book and they all are intended to be true expositions of the Word of God. The books include: the three Ecumenical Creeds (the Apostles' Creed, the Nicene Creed, and the Athanasian Creed), the Unaltered Augsburg Confession, the Apology of the Augsburg Confession, the Smalcald Articles, the Treatise on the Power and Primacy of the Pope, the Large Catechism of Luther, the Small Catechism of Luther, and the Formula of Concord.
These books provide a definition for anyone that seeks to know what it means to be Lutheran. They are not the Word of God, but they do provide a correct interpretation of the Word of God. They do not add to or subtract from the validity or purposes of the Word of God.
As important as Martin Luther was for the Reformation of the church in the 16th Century, Lutheran churches do not follow Martin Luther. We follow the Word of God. The confessions norm our reading of the Word. The confessions provide a frame to interpret the Word of God for our own times and places. So therefore, in this manner, we believe the good news of Jesus Christ is at the center of proclamation and theological reflection. As believers in Jesus, we are always aware that are witness of Christ's love to other believers and those outside the faith takes place in the presence of and through the power of the Holy Spirit.
Lutherans, in a wide variety of situations, find the documents of our confessions helpful to define what Lutherans mean when they speak of Christ's church and its teaching. We do not have a state authority defining the church. We do not have a charismatic leader receiving visions from God defining our church. We do not have liturgy serve as the framework for our identity. The framework and foundation for the confession of the Christian faith in our times remains centered on the good news of Jesus Christ.
You can read the Book of Concord online: http://bookofconcord.org
Concordia Publishing House prints a wonderful readers edition that includes helpful notes and historical introductions.
The standard English academic edition is edited by Kolb and Wengert.