How to send group mail in Outlook to multiple recipients, but have each recipient see their own name?

I think you are looking for the add-in called Send Personally:

Send Personally is the add-in for Microsoft® Outlook® designed to send individual emails to a great number of recipients via Microsoft Outlook 2010 / 2007 / 2003 / XP / 2000. This add-in for Outlook offers you an alternative method of sending personalized emails from Outlook: separate messages are being created for each recipient. The final recipient will receive no information about any of the other recipients. Moreover, he/she will see only his/her name and address in the "To" field, as if the message is sent to him/her only.

Note: You can also achieve the same result by using the Mail Merge feature in Outlook. This method does exactly what the Outlook add-in does and its FREE.

Simply putting all the recipients in the Bcc: field should do it, although that way they won't see their name in the To: field. More information on Bcc at the Microsoft Office website.

Alternatively, you could use a mail merge. Again, more information can be found at the Microsoft Office website.

There is a free Send Messages Personally add-in from Outlook Freeware (starting with 'S') and a commercial product, ReliefJet Essentials for Outlook, (I'm one of its developers and its name starts with 'R').