Some CB sidebanders use a designation of World Wide. For instance, there is John, a CB operator in South Carolina, who refers to himself as World Wide 142. Nice fellow.
On the other hand, there are still several SSB CB radio clubs operating who use club name prefixed call numbers. One of those is TWRC, or The World Radio Club. Operators who identify with the club while DXing will refer to themselves by the club name and their assigned number.
For instance, I am World Radio 183 (or phonetically Whiskey Romeo 183).
Membership in the CB clubs is generally as easy as a request, it is more difficult to obtain membership in TWRC. PM me if you are wanting to know more about that.
As has been said TWRC is not affiliated with WWRF.
I believe you are correct that there is no CB club, only an Amateur club associated with this forum, WWRF.