Name change after marriage with a green card

[Nephron]

Hello all,
My husband and I have a green card, and got married in 2012. I am planning to take my husbands last name. I went to the SSA office, and was told that I need to first get the name changed on my green card. I have family on H1 visa that got their last name changed on the basis of marriage without having to change it on the Visa. I was wondering how is a green card different in that sense? Has anyone here gone through this process?
Thanks for your help.

[Cory Trevor]

I don't have any first hand experience with this particular situation. I would guess that the Social Security office is correct. H1 Visas are much different than green cards, so it does not surprise me that the renaming regulations are different. I know that it can be done because my sister-in-law changed her maiden name, and she had a green card.

http://www.honoluluimmigration.net/immigration-lawyer