I've been a member for more than 8 years.  I find such persistent charges of secrecy silly, almost lurid.    

There is what's called "privacy"...as in it's a "private" matter for a person to choose to get formation from Opus Dei, so there is no "publishing of members" by OD itself.  Privacy is not secrecy. 

If a member chooses to tell other people where he/she gets spiritual direction, or doctrinal formation, or spiritual formation, etc, then they certainly can. 

See the Crux article today written by John Allen's wife; she's Jewish and not a member of OD. 

Hyper-secrecy...a rather callow point.