While you have only one primary email address--the one you use to log into Gmail with--you may have several "alias" email addresses as well depending on what's been setup for you.
These so called "aliases" allow you to receive email sent to a different different in your primary mailbox. Similarly, with a little bit of setup, you can also send "from" an alias address.
Please note: an alias must be setup for you by an administrator before these instructions will work for you.
Once setup, here's how to send from another address:
In Gmail, head to the "gear" icon and choose "settings."
At the top, click "Accounts" and click on "Add another email address."
In the pop-up window, enter your alias email address. Make sure you leave the "treat as alias" box checked.
Click "next step."
Assuming the alias has been setup for you by an administrator, you'll be returned to the settings window. At this point, you can close out of settings to return to your inbox unless you'd like to make this new address your default address. If that's the case, click "make default" by your new alias address.
For good measure, you may want to set your preference whether you always reply from your default address or if you'd like to reply from the address the message was sent to. I prefer the latter. That simply means if the message was sent to Neil.Finn@indinero.com, my reply will come from that address. If it was sent to nfinn@maccounting.com, my reply will come from that address.
Now when you compose an email, you can click your "from" address drop-down and select any alias you have setup and the message will go out from that address.
Happy emailing!