Name change / green card differs from passport

[tmg27]

I legally changed my first name and added a middle name last year and finally sent an i90 for Green card replacement 2 weeks ago. Biometrics appointment was today, so that seems to be fast. But my question is a different one

Once I get the new green card, my new name will be on it as well on my drivers license. My German passport will still have my old first name.

I have to travel quiet a bit internationally (Canada this year)

Is simply showing them the name change order good enough? It had pleased ATF, TSA, Department for public safety etc so far.

Any experiences?

[Enub4]

I guess if you travel with all the documents to prove that you are the same person and changed your name, you will not have much problems, maybe some delay while the officer check all the documents.
Is getting a new German passport with your new name too hard? That will make your frequent travel easier.