To log into a Steam ID, you use a username, not an email, unless you specifically set the login username as the email.
One email can be tied to multiple Steam IDs (even if one of them has the email as the username for login).
Changing the display name of a Steam ID does not change the Steam ID or the username to log into it. Multiple Steam IDs can have the same display name; they are not unique and can be changed at will.
You must be able to log in to the Steam ID linked to your Bungie.net profile in order to disable Cross-Save or unlink it. If you cannot log into that specific Steam ID, you'll be unable to do disable Cross-Save or unlink it. Simply changing the display name of another Steam ID will not allow you to log into a different Steam ID.
To my knowledge I should only have had one ID and one active email and I changed my display name once. When I go to my profile I don't see my original ID as an alias.