Middle Name in Green Card, but not in Passport

[my_nick]

Hello,

I just received my green card.
USCIS added a middle name (Initial only) to it.
That middle name came from my birth certificate translation from Russian.
In all my other documents including my passport, I do not have a middle name.
Would I have any problem with that mismatch in the future ?
For example with SSN, DMV, entering the US (since the middle name doesn't appear in the passport) ?

Thanks!