Unfortunately not as this how PayPal associates you with your account.
One suggestion would be to add a new (shorter) email address and make that one the Primary.
One other possible work around would be if you have a Business Account. Business Accounts have a feature called Multi-User Access. This feature is for businesses who have the need to have more than one person access an account. The owner of the account can assign user names (not email adddresses) and passwords to the individuals they want to access the account. In addition, the owner then assigns rights or permissions where as they control what the people can do within the account. To lean more about this feature, check out this user guide:
https://www.paypalobjects.com/webstatic/en_US/developer/docs/pdf/pp_merchantsetupadministrationguide...
