There is 2 things you have to configure. One to make sure that your users email address is always in the form of @anyname.com. And 2, that you exchange server exepts email for the domain anyname.com.
1. In the recipients policy (Open up System Manager, Expand Recipients double click on both the default policy and the site policy, under the email addresses policy tab) make sure you have anyname.com set as default.
2. In the SMTP connecters properties (in System Manager Expand Administrative Groups > Site name > Servers > Server Name > Protocols > SMTP > Default SMTP Virtual Server, right click on Default SMTP Virtual Server and choose properties, click the delivery tab, click advanced) make sure that in the box Fully-qualified domain nameyou have anyname.com (you can put any host name in the form of Host.anyname.com if you want).
3. Expand Recipients > Recipient Update Services, right click on all the items on the right, and choose both Update now, then Rebuild and answer yes on the rebuild question.
In your case where your email is held by your ISP until you pick it up. You have to find out if the only way the will let you have the email is thru POP or will they also give you SMTP? If they only give you POP then you will have to use a 3rd party program to collect the POP email and distribute it in you exchange mail boxes, one such program is POPBEAMER.
If they allow for SMTP relay then it is best that you configure your exchange server with your ISP tech support.