The FDCPA cuts two ways on this issue, Mea. A collector must make "meaningful disclosure" of its identity yet respect the privacy of whoever is named on a debt account. Hence the obfuscation in messages and demands for identifying data in live calls. Privacy is about the only consistently followed rule, as being shadowy works in their favor to make call targets anxious.
There are case rulings which say that collectors cannot break one law to follow another, but this is something without a definite answer within the FDCPA as written.