@ TNIB
Try to use the Bible to get her to reason.
Ask her why Rutherford decided to capitalise on the generally accepted Divine name of God, instead of retaining the God-given name of 'Christians'? (Acts 11:26)
You can then ask her to read the following Scriptures to prove to herself that she is Witnessing for Christ!!
You could also mention to her the change in the Org's letterhead in recent years to "Christian Congregation of Jehovah’s Witnesses".
Matthew 10:18 - "YOU will be haled before governors and kings for my sake, for a witness to them and the nations.
Mark 13:9 - and YOU will be beaten in synagogues and be put on the stand before governors and kings for my sake, for a witness to them."
Acts 1:8 - "You will be witnesses of me;
John 1:15 - "John bore witness about him..." [JESUS]
John 5:37 - "the Father who sent me has himself borne witness about me."
John 8:18 - "the Father who sent me bears witness about me."
John 15:26,27 - "the spirit of the truth, which proceeds from the Father, that one will bear witness about me; and YOU in turn, are to bear witness." [exactly as the spirit bore witness - about me];
Acts 10:39 - "And we are witnesses of all the things he [Jesus] did..."
Acts 10:43 - "To him [Jesus] all the prophets bear witness, that everyone putting faith in him gets forgiveness of sins through his name.
Acts 11:26 - "the disciples were by divine providence called Christians."
Acts 13:31 - "and for many days he [Jesus] became visible to those who had gone up with him from Gal´i·lee to Jerusalem, who are now his witnesses to the people.
Acts 22:15 - "because you are to be a witness for him [Jesus] to all men of things you have seen and heard."
Acts 22:20 - "and when the blood of Stephen your [Jesus'] witness was being spilled..."
Acts 23:11 - "For as you have been giving a thorough witness on the things about me in Jerusalem..."
Acts 26:16 - "For to this end I [Jesus] have made myself visible to you, in order to choose you as an attendant and a.......(respecting me) witness
1 Corinthians 1:6 - "even as the witness about the Christ has been rendered firm among YOU..."
1 Tim. 2:6,7 - "who [Christ] gave himself a corresponding ransom for all—[this is] what is to be witnessed to at its own particular times. For the purpose of this witness I was appointed a preacher and an apostle..."
2 Timothy 1:8 - "Therefore do not become ashamed of the witness about our Lord.. [Christ]"
1 John 5:9 - "the witness God gives is greater, because this is the witness God gives, the fact that he has borne witness concerning his Son."
Revelation 1:9 - "....came to be in the isle that is called Pat´mos for speaking about God and bearing witness to Jesus."
Revelation 12:17 - "And the dragon grew wrathful at the woman, and went off to wage war with the remaining ones of her seed, who observe the commandments of God and have the work of bearing witness to Jesus."
Revelation 17:6 - "And I saw that the woman was drunk with the blood of the holy ones and with the blood of the witnesses of Jesus"
Revelation 19:10 - "But he tells me: "Be careful! Do not do that! All I am is a fellow slave of you and of your brothers who have the work of witnessing to Jesus. Worship God; for the bearing witness to Jesus is what inspires prophesying."
Revelation 20:4 - "Yes, I saw the souls of those executed with the ax for the witness they bore to Jesus."