Interesting idea. I found lots of quotes showing that it's the anointed who bear the name "Jehovah's Witnesses".
“The Nations Shall Know That I Am Jehovah”—How?, pages 307, 319, 320
In appreciation of this, the anointed remnant, in the year 1931, embraced the Scripturally based name, “Jehovah’s witnesses.” … Realizing more keenly than ever that he was taking out of all nations a “people for his name,” the anointed remnant saw good to identify themselves before all the world by the name drawn from the Holy Scriptures, Jehovah’s witnesses. … When the name, Jehovah’s witnesses, was first embraced by the anointed remnant in the year 1931, the question arose in the mind of many worldly observers: “Will the name stick?”
Watchtower March 1 1996, page 14
These anointed Christians have always kept Jehovah’s name to the fore, but especially so since 1931, when they adopted the name Jehovah’s Witnesses.
Watchtower November 1 1993, page 9
Without any doubt at all, it was the small body of anointed brothers of Jesus who in 1914 were known as the Bible Students but since 1931 have been identified as Jehovah’s Witnesses.
Watchtower November 1 1976, page 663
So now, with the words of Isaiah 43:10 ringing in their ears, those anointed champions of Jehovah and of his kingdom by Christ took up the Bible-supported name “Jehovah’s Witnesses.”
Paradise Restored To Mankind—By Theocracy!, page 364
In turn, the faithful anointed remnant has said: “Jehovah is my God.” Outstandingly so since July 26, 1931, when those of this anointed remnant embraced the name “Jehovah’s witnesses.”
Watchtower March 15 1973, page 168
In appreciation of this, the anointed remnant, in the year 1931, embraced the Scripturally based name “Jehovah’s witnesses.”
Watchtower December 15 1971, page 750
It was this active body of dedicated, anointed Christians who, in the summer of 1931, embraced a name to distinguish them from Christendom’s sects, namely, Jehovah’s witnesses.
And these two quotes actually indicate that "Jehovah's Witnesses" and "the other sheep" are two different groups (it's actually quite clear in German):
Watchtower December 15, 1990, page 13
Moreover, as early as 1932, The Watchtower pointed out the responsibility of the “other sheep,” in their turn, to say, “Come!” (John 10:16) In its issue of August 1, page 232, paragraph 29 stated: “Jehovah’s witnesses now have the zeal like to that of Jehu and they should encourage the Jehonadab class [other sheep] to come along with them and to take some part in proclaiming to others that the kingdom of God is at hand.”
Watchtower December 15 1982, page 22
Noteworthily, their fellow worshipers at God’s temple, the “great crowd” of Christ’s “other sheep,” display the same unquenchable love that binds Jehovah’s Witnesses of today together so perfectly.