Try this:

till version 9: cr.dbname

after 9: self.env.cr.dbname

Once you've logged into a database, the URL will contain db=XXXX where XXXX is your current database.

if you need it from inside the code... then
db_name = self.pool.db.dbname (in v7)

or from browser look in the link like ivan explained...
 

In code, for version 10, its self.pool.db_name