As Ove touched on, you can set up 'accepted' mail domains - completely different to your internal active directory domain. This is done in the Exchange Management Console:
Organization Configuration -> Hub Transport -> Accepted Domains.
If your AD domain is companyname.bos, you can easily add in accepted domains for companyname.com, companyname.net, entirelydifferentdomain.com.au, and so on.
You won't need to rename the AD domain.
SSL; Exchange will generate a self signed certificate for the exchangeserver.companyname.bos domain, however you can also use a self signed FQDN for exchangeserver.companyname.com, or, recommend to get a properly recognized SSL certificate from somewhere like GoDaddy.com to prevent any 'unrecognized SSL certificate' errors.