Rutherford introduced the distinguishing name Jehovah's Witnesses in the Watchtower 1931 September 15 and October 1. Rutherford used Isaiah 62:2 as his principle reference.
Isaiah 62:2 "And you will actually be called by a new name, which the very mouth of Jehovah will designate."
This was poor choice of scripture as just 2 verses later the name given is not Jehovah but Hephzibah.
Isaiah 62:4 "… but you yourself will be called (Hephzibah RSV) My Delight Is in Her …."
This erroneous reasoning was later corrected, and
Isaiah 43:10 brought to prominence instead.
"Although the evidence points persuasively to Jehovah's direction in selection of the name Jehovah's Witnesses, The Watchtower (February 1, 1944, pp. 42-3; October 1, 1957, p. 607) and the book "New Heavens and a New Earth" (pp. 231-7) later pointed out that this name is not the "new name" referred to at Isaiah 62:2; 65:15; and Revelation 2:17, though the name harmonizes with the new relationship referred to in the two texts in Isaiah." Jehovah's Witnesses - Proclaimers of God's Kingdom p. 156 Footnote
It is admitted in Jehovah's Witnesses - Proclaimers of God's Kingdom p.152 "Isaiah 43:10, 12 was never discussed in any detail in The Watch Tower during its first 40 years of publication." It was in 1926 that the importance of the word Jehovah was introduced by Rutherford. "Especially since the year 1926 they have been making known the name of the heavenly Father of the King Jesus Christ, even going to the extent of embracing the name "Jehovah's witnesses" in the year 1931." God's Kingdom of a Thousand Years Has Approached p. 288 Further effort to shift attention from Jesus to Jehovah was made in 1939 when The Watchtower and Herald of Christ's Kingdom was renamed The Watchtower Announcing Jehovah's Kingdom.
The Watchtower gives precedence to the name Jehovah's Witnesses based on Isaiah 43:10 in favour of the wealth of New Testament guidance to be "witnesses of me"- Christ Jesus. (Acts 1:8)
Luke 24:46-48 "In this way it is written that the Christ would suffer and rise from among the dead on the third day, 47 and on the basis of his name repentance for forgiveness of sins would be preached in all the nations-starting out from Jerusalem, 48 YOU are to be witnesses of these things."
Acts 10:43 "To him all the prophets bear witness, that everyone putting faith in him gets forgiveness of sins through his name."
Hebrews 12:1-2 " … we have so great a cloud of witnesses surrounding us, ... as we look intently at the Chief Agent and Perfecter of our faith, Jesus."
Revelation 17:6 "…the witnesses of Jesus."
Russell remained opposed to being known as anything other than a follower of Christ.
"It was an evidence that those Corinthians, who took the party names, had never really appreciated the oneness of the Body of Christ; that they did not really appreciate that Christ is the only head, leader and standard; and that his is the only name by which his followers should recognize themselves and each other. Where scoffers apply a name in derision, it is not the fault of the faithful. But the true, loyal soldiers of the cross, should never own or recognize such a name. Instances of names so originating are Methodists and Baptists, both of which were first given in derision, but were afterwards adopted as party names, representing sects, factions, or divisions in the body of Christ. All true teachers are not only sent by Christ but receive their instructions from him; and any man who attempts to put his own or any other name upon all or any portion of the church is an opponent, an adversary to the true and only Lord and Head of the church." Zion's Watch Tower October 1888 p.3