I'm in a similar situation. I have 5 first names, only one is listed in my passport (the passport I used to get my visa), and I can't see myself having used the other names on my marriage certificate (I never use the other names) - it was never even discussed at the interview. If you want your middle name listed on your green card, you'll have to update your passport. If you do not mind using only the names in your passport, it's a non issue. Just don't forget to disclose it in other names used, when requested.