How to deal with RMAN-06004: ORACLE error from recovery catalog database: RMAN-20005: target database name is ambiguous

It turned out that the my RMAN session didn't know which DBID to perform the requested command against.

I checked my incarnation list, and observed the following:

RMAN> list incarnation of database;


List of Database Incarnations
DB Key  Inc Key DB Name  DB ID            STATUS  Reset SCN  Reset Time
------- ------- -------- ---------------- --- ---------- ----------
1       198     PTADB01  2645386576       PARENT  6275306386559 10.04.11
1       2       PTADB01  2645386576       CURRENT 6278643127311 20.04.11
681     923     PTADB01  2663743751       PARENT  6275306386559 10.04.11
681     682     PTADB01  2663743751       CURRENT 6435835146938 16.11.11

Note how two of my incarnations are marked as being PARENT. Never saw this before.

A quick search on the internet pointed me to setting the DBID explicitly, so I vierfied that the DBID listed in the incarnation list above was indeed correct, by checking the backup logs files, and set it in the RMAN session:

RMAN> set DBID=2663743751;

So when the database name is not unique in the recovery catalog, you need to point out which one to use before RMAN can work.
The restore now worked, and the database could be mounted.