The fact that mail names do not show up when mailing to the list is not a good reason to need a system mailing list, since you could accomplish this by having a personal mailing list but using the mailing list in a Bcc: header. Bcc is a notation for blind carbon copy, signifying that the message will be sent to the recipient, but the recipient will not be listed in the message header. If you do not know how to do this with your particular mail program, please mail to root specifying that you want to use Bcc: and also noting which mail program you use.
Please do not use this form unless it is needed. A system mailing list is only needed if more than a few people are going to mail to the list; especially if people outside the list are mailing to the list. If just few people need the list, it could easily be maintained in personal mailing lists in their own mail setups.