Anonymous to your friends, not anonymous to the service or law enforcement. There should be a word for this... maybe "pseudoanonymous"?
I guess I don't get the use case, as I would generally think anonymity from people I already am acquainted with would be the least useful (to me).
It really seems like there is an entire class of applications that have risen to answer problems that exist solely because of Facebook's dominance and policies (ie: data collection/retention policies and insistence on identity).