From what I understand the 'Friends' was the term used back in Russell's era to distinguish the many people who supported his ideas as presented through the WTBTS publications.
Russell was often asked to meet with and present his beliefs to these early followers (who eventually formed the International Bible Students Association). Since transportation and housing was necessary as well as a warm and enthusiastic welcome he began to refer to those supporters as The Friends.
The tern stuck here in the USA and is still recognized and in use in an informal way.