Must full text index catalog name be unique on same SQL server? (MSSQL 2005)

Consider there is one MS SQL server 2005 instance with 3 databases on it ... Dev, RC and Production. All of them have (more or less) the same schema. All of them have a "same" table with full text index on it.

1. What happens if the name of full text index catalog is the same on all 3 databases?
2. Do they share the same physical catalog?
3. Is it any better (performance) to have unique catalog name on each DB?

It seams MSDN Create fulltext catalog does not give a good answer to that.

From stackoverflow

• On SQL2005 the catalog names do not need to be unique. On the file system SQL will add a 4 digit number to end of the name to make it unique (eg. "ft_Catalog" becomes "ft_Catalog0000", "ft_Catalog0001", etc).

  I prefer to name the catalog so the database name is included: "ft_cat_[DATABASENAME]". Makes looking at the file system easier.