Find current database name from db handle

[Kostas Chatzikokolakis]

Hello,

I'm using a dbi handle that is shared between many packages in my
code. Some package might do a "USE db_name" to change the current
database of the connection. Can I retrieve the current database name
from the handle, either from DBI or from the DBD::mysql driver
(without querying the server)?

Thanks in advance,
Kostas