Even a non denominational congregation can "not" be a congregation without faith and confession in Jesus.
Romans 10:9
9That if you confess with your mouth, "Jesus is Lord," and believe in your heart that God raised him from the dead, you will be saved
It is not about offending anyone. Satan plants that evil lie in the minds of people that calling yourself a Christian is a bad thing. Some people don't want to be called Christians, because they have their own set of beliefs. That is totally in contradiction of God's Word.
If we follow Jesus, we are Christians.
The definition of the word Christian:
The term Christian means "belonging to Christ" and is derived from the Greek noun Χριστός Khristós which means "anointed one," which is itself a translation of the Hebrew word Moshiach (Hebrew: משיח, also written "Messiah"), (Arabic it is pronounced Maseeh مسيح). ...
May I be a Christian dear Lord! I am a Christian, I belong to Jesus! Amen!
Some more verses from God's Holy Word:
1 Peter 4:16
However, if you suffer as a Christian, do not be ashamed, but praise God that you bear that name.
Acts 11:25-26
25Then Barnabas went to Tarsus to look for Saul, 26and when he found him, he brought him to Antioch. So for a whole year Barnabas and Saul met with the church and taught great numbers of people. The disciples were called Christians first at Antioch.
Romans 1:6
And you also are among those who are called to belong to Jesus Christ.