Hello Tanya O,
You can contact admin, let admin help create an alias for shared mailbox in Microsoft 365 Admin center -> Groups -> Shared Mailbox:
Besides, please be noted that even if we can create alias for shared mailbox, when recipients receive emails from it, they’ll still see the primary email address.
Since Shared mailbox doesn’t need any license, you could consider create a new shared mailbox instead. We by default has Full Access permission as a member of it and will see it be automatically mapped to Outlook desktop client, even if we only use Outlook Web App, we can still access it by manually adding shared folders: Open and use a shared mailbox in Outlook on the web
Best Regards,
Anna