Yes, you can configure SSPR to use custom attributes for authentication. You need to configure Username Search Filter under Settings > LDAP Directory in Configuration Manager. For more information about how to configure, see Configuring LDAP Settings.
Example configurations:
(&(objectClass=inetOrgPerson)(myCurrentName=%USERNAME%)
In this example, the username value entered in the login page should match the attribute myCurrentName and the matched object should be of type InetOrgPerson.
(&(objectClass=person)(|(myCurrentName=%USERNAME%)(samAccountName=%USERNAME%)(cn=%USERNAME%)))
In this example, the matched object should be of type person and the username value on the login page should match with myCurrentName, samAccountName, or CN attributes.