Steven,
Sorry -- I failed to note you are using Panther and not Tiger, re: Edit Email Aliases.
I somewhat expected your purpose, but I wanted you to lay it out. Do you also have other accounts, such as POP, and the use of another SMTP?
The issue you are encountering is in the general category of using different Full Name info for the same email address, or for an alias of your .mac, prior to the introduction of Tiger (10.4.x) -- with the Mail in Tiger, you can send from your .mac alias, and it will include no info other than the email address, itself. All this is done from within the one .mac account setup in Mail.
In Panther (10.3.x), the problem does not exist, except when sending, since you can give the address without any name (or names) in front to anyone, and you will receive it amongst the messages of your main .mac account Inbox.
In Panther, I developed one method to send with a .mac alias. This was done by adding the .mac alias as a second address (entered by typing a comma, and then the new address) into one of my POP accounts, which sends with the SMTP provided by my ISP. The latter is the key, because it is the .mac SMTP that refuses to send with the alias. Also, note that not all ISP will permit sending from a domain address that is not theirs, but many will. Here again the Full Name would need to be edited to disguise your ID.
Then while in Compose, chose the .mac alias address in the pull down menu for sending addresses. The message sent will be saved in the Sent mailbox for the POP account, and not your .mac account.
Another way is to set up a new POP account, with the Username of the .mac alias as Username, and both deselect to include when automatically checking for new mail AND take the account Offline. This may work for you, if you have an email account with your ISP, and the use of the ISP's SMTP.
Another method offered was found at:
http://discussions.apple.com/thread.jspa?messageID=607268򔐤
but this method may not cure the Full Name issue, as you would prefer.
HOWEVER, if .mac will now send with an .mac alias in Tiger, there may be a way to do in Panther. Since I still have Panther operating on one Mac, I will experiment, and get back to you. But this may not be possible, based upon the statements in the following support article:
http://docs.info.apple.com/article.html?path=Dotmac/Mail/en/mac45.html
PowerMac G5 Dual 2.5, iBook, and QS G4 867 Mac OS X (10.4.3)