Hello,
If I remember correctly, it wouldn't show the option of replacement card if non-citizen. Citizen account also has social security benefit section.
I logged in again today and found the 'non-citizen' part has disappeared. The page also shows retirement and benefit etc. I guess it has been updated to citizen account.
yeah, I think you are right. For people who applied immigration process, it is recommended to change name after finished the process. Additionally, like you said, it is free to do so at the oath.