Seems to me they were acting properly in attempting to identify you before discussing the nature of the debt. Once they establish your identity, you can make them specify, in writing, all the particulars, and you can request, in writing, that they stop calling you.
I am not a lawyer, so I'm going to quote the Wikipedia article on the FDCPA. Under Prohibited Conduct it includes:
Communication with third parties: revealing or discussing the nature of debts with third parties (other than the consumer's spouse or attorney) (Collection agencies are allowed to contact neighbors or co-workers but only to obtain location information;[18] disreputable agencies often harass debtors with a "block party" or "office party" where they contact multiple neighbors or co-workers telling them they need to reach the debtor on an urgent matter.)
Seems to me they were acting properly in attempting to identify you before discussing the nature of the debt. Once they establish your identity, you can make them specify, in writing, all the particulars, and you can request, in writing, that they stop calling you.
Links to the actual statute are in the Wikipedia article.