Hello,
not with the OOB functions of FIM.
I'm not quite sure if it is possible by writing a custom activity and modify the password reset portal, but i think this will be to much efford for this functionality.
Could be easier to search for a "ready to deploy" product for that or writing a custom web application which will query AD and sends back username to the given mail address.
And a easy solution with no-code !!!:
Since users dont forget their mail address, what about having the email also set as the UPN, since you can use UPN (email) to reset your password.
With this there is maybe no need to recover the username.
If your AD DNS namespace does not match your mail dns namespace you can use alternate upn-suffixes in your AD.
However this will impact the user logon behavior.
Regards
Peter