Can Log filename include database name?

I am currently using a log with the file name format:
log_filename = 'postgresql-%Y-%m.log'

Is there any way to change the filename do start witht he database name?

For now just added to add the database name to each line, but it would be
usefull to have each DB written to it's own file. Or even better to be able
to specify on a per database basis whether to log or not.