Different LAST NAME in different passports (US green card application)

Hi

I am a US citizen with a dual nationality. My last name in the US passport is different than my last name in my other passport, because my grandfather stopped our family name at a different grandfather when he obtained his US passport which I inherited from him. Now I am applying for my husband for a green card, but my marriage certificate has my name with the different last name to that of my US passport. Is this going to cause me problems or do I have to mention it in the other name known by section or present more evidences?

Thank you for you reply!

If there is a discrepancy, then what makes you think that giving no explanations wouldn't cause you problems?

Thank you for your reply!
You are right I should include the explanation , although it may lead to more interviews and requires more evidence.