There is a way to do what you are describing BUT it requires setting up separate accounts in Outlook.
I'd like to use your example above and expand upon that. Assuming that websitename@mydomain.com is your main email account that is configured as a catchall mailbox for your domain. Let's also assume that you have Outlook configured to send and receive email from that address.
Although the mailbox described above will receive emails to any username at mydomain.com you will still only be able to SEND as websitename@mydomain.com. In order to be able to send mail as, for example sales@mydomain.com you have to add a second, new account to your Outlook configuration.
Go to Tools--->Account Settings and select the E-mail tab. Click New... and select Pop3 and hit Next>
Enter the name and email address that you want to send email as.
Example:
Your Name: Sales Director
E-mail address: sales@mydomian.com
Don't worry about password at this point. We will override password settings in a subsequent step.
Hit Next>
Auto Configuration will fail at this point. That is OK. Click Manually Configure E-mail Settings and hit Next>
User Information
Your Name: Sales Director
E-mail Address: sales@mydomain.com
Server Information
Incoming mail server: localhost (this is an outgoing-only account incoming is handled by catchall)
Outgoing mail server (SMTP): (provide smtp server hostname here)
Login Information
User Name: sales
Password: (leave blank)
click More Settings...
in the Internet E-mail Settings dialog click the Outgoing Server tab
check the checkbox for My outgoing server (SMTP) requires authentication
click the radio button for Log on using
User Name: websitename@mydomain.com
Password: (your password for websitename@mydomain.com)
Save all chagnes and test settings. Incoming mail service will FAIL for this account. That is ok because websitename@mydomain.com is already your incoming mail catchall. it's essential however that your outgoing mail server passes ok. When this is done test your new address by opening a New E-mail Message in the send header you will see that you have the ability to select send From... multiple email addresses. Select sales@mydomain.com and send yourself an email.
You will have to repeat this process and add additional accounts for every email address you want to send from.