Name mismatch SSN# from previous J-1 <> new J-1

[kartoffelsalat12 0]

Dear all,

My family name has a German umlaut " Ü ", e.g. Müller.

I have previously been to the US with a J-1 visa in which my name was stated on form DS-2019 with an " U " - Muller. This is also the name that was used for my SSN#.

However, the name in the machine-readable part of my passport comes with an " UE " - Mueller.

My new DS-2019 (for a new J-1 program) states my name with an " UE " - Mueller, i.e. just as in the passport.

Will I be able to change the name on my SSN-record to " UE ", as long as I provide my passport, both current and former DS-2019, etc.?

Or will I be running into trouble with my new employer when giving him my old SSN (the number, which obviously can't be changed)?

Any help is appreciated!