they changed the name because after 1916/1917 when Rutherford did the force takeover, many other splinter groups retained similar names and literature from Russell. To differentiate from the rest, a name change was in the works. Specifically the thorn was from the Dawn Bible Students Association formed in 1929. Changing the name gave a sense of ownership to watchtower. Even their own publications manage to say this is the reason for the name change:

JE pp. 8-11

"In 1931 the Bible Students adopted the name Jehovah’s Witnesses. Prior thereto they were known as Bible Students, International Bible Students, Millennial Dawn people, and Watch Tower people. They were even nicknamed Russellites and Rutherfordites. None of these names properly identified them. While the name Christian, given to Jesus’ disciples by divine providence in the first century, was certainly applicable, it was also being used by many groups following false teachings. To distinguish themselves from the millions of nominal Christians, there had to be a name that would distinctly identify Christ’s true followers in this day"