Changing domain connected with hosting

Hi,
I'm using hosting in personal option which was created with my domain (lets call it mydomain.biz)
Under this hosting I can manage hosting and mails - also for this domain.
My question is, if there is possible to change the hosting form mydomain.biz to mydomain.pl (I am a owner of mydomain.pl).
I don't want to do redirection - I want to have the all functions (with mails) available for new domain.
Is it possible?
If not, Is there possible to redirect mails between domains? form mydomein.pl to my domain.biz?