exchange 2013 - server2012 domain name and exchange2013

I have a server 2012 with a AD setup with domain.local setup.
I would like to add exchange to our new server 2012 just added.
our current setup:

1 server 2012 domain setup domain.local with AD
1 server 2012 (new) would like to add exchange on.
hosted emails(name.net), and website from godaddy (website name.net)

I would like to setup an exchange server to get away from godaddy emails.
but leave the website there for now.

Should i rename my domain.local to .net?

Any help from experts on what they would do would be appreciated.

Thanks