Since 2012 (v 1.11), Wget allows renaming files according to server's instructions, as given in the HTTP header "Content-Disposition". All it takes is adding the flag "--content-disposition" to wget's invocation.
With that flag the BBC podcast http://open.live.bbc.co.uk/mediaselector/5/redir/version/2.0/mediaset/audio-nondrm-download/proto/http/vpid/p033zrky.mp3 is renamed as Documentaries-20151001-SpainsBattleForTheBull.mp3.
I sugest we get "--content-disposition" activated in Podget.
Done.