How do I keep the individual names on a Group List from appearing on each email?

I am setting up a large mailing list on Eudora and do not want to show all of the names on each email that is sent out.

Use BCC. That stands for Blind Carbon Copy. Each recipient will get a copy of the email, but none of them will see the other recipients. You will need to have at least one email address in the "To" box, so if you don't want anyone to see anyone else's name, then for the "To" just put in your own email address.