SSN# for ECFMG Application

Hi,

I have a brief question regarding the ECFMG application.

My (german) name is officially spelled with an ü-letter (both in passport and on medical diploma, ..).

On my passport it also states my name with an "ue" instead of an "ü" in the machine-readable part, so this would be the version I would enter for my ECFMG record, and I would include a photocopy as verification to show that both spellings are correct (was also used for a previous US visa).

However, I already have a Social Security No., assigned to my name spelled with "u" instead of "ü" (note that this is different from what I will use for my ECMFG record), because that was what was stated on my DS-2019 back then.

My question is, whether I should enter this SSN# in the application process, or whether I should rather not mention it so as to avoid any confusion (but might this cause problems in the future)?

Thanks!

Just to make sure:

Official name on Passport, Medical Diploma, ...:
Müller

Official name in machine-readable part of passport, to be used for ECFMG (also used for previous US visa):
Mueller

Name used for SSN:
Muller