Looking at the docs, database handles have a three attributes that sound useful. It turns out that all three are useful. I don't know how you could have missed them all.

$dbh->{Name}
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$dbh->get_info( $GetInfoType{SQL_DBMS_NAME} );
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$dbh->{Driver}->{Name}
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The DBI docs are pretty long, though.. It's tempting when first using it, to just read what you 'think' is essential to you, and skip all the 'extra' stuff.

Still no excuse for RTFM! But.. I'm feeling a little leeway here on not catching that.. (no?)

It's tempting when first using it, to just read what you 'think' is essential to you

It sounds like you're saying that's a bad thing, but that's exactly how I got the answer.

The DBI docs are pretty long, though..

When wanting a property of a database handle, look at the index for database handles.

    * Database Handle Methods
          o clone
          o data_sources
          o do
          o last_insert_id
          o selectrow_array
          o selectrow_arrayref
          o selectrow_hashref
          o selectall_arrayref
          o selectall_hashref
          o selectcol_arrayref
          o prepare
          o prepare_cached
          o commit
          o rollback
          o begin_work
          o disconnect
          o ping
          o get_info
          o table_info
          o column_info
          o primary_key_info
          o primary_key
          o foreign_key_info
          o statistics_info
          o tables
          o type_info_all
          o type_info
          o quote
          o quote_identifier
          o take_imp_data 
    * Database Handle Attributes
          o AutoCommit (boolean)
          o Driver (handle)
          o Name (string)
          o Statement (string, read-only)
          o RowCacheSize (integer)
          o Username (string)
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I got three possible answers from that. Three quick clicks indicates all three fulfill the OP's requirements.

That's not long. That's among the shortest amount of reading I've had to do to find a function. And I found three!

many thanks. ++