I prefer to call it JW religion, or JW organization. And, I still refer to "The Society" when talking to other JW's so that there's no doubt I'm referring to the HQ of JW's--most elders and rank & file now call this "The Branch."
For me the appeal was that they were under ban in the country I was living in under a dictator. Preaching work was illegal, and they were thrown in with other government undesirable religions, which were usually just called the "Protestants" (pronounced with a half raised lip as if smelling something foul).
The WT literature talked a lot about God and how He had a wonderful purpose for mankind. I was suckered in and swallowed their whole line, hook and sinker. I thought it was the Truth--I was convinced of it until tragic circumstances burst the dream bubble. Now I'm still in due to having family that is very faithful to the WT.