how important is name on the Social Security card?

Question

lets say my wife's last name is Gonzales but the ss card shows Gonzales-Garcia. i would assume this would be her new whole last name because of the dash. she Has been using Gonzales in the past. Does this means she has to use Gonzales-Garcia from now on and for everything. Would it be a big deal if she uses just Gonzales as last name in further documents without changing the name on the SS card. or would there be a conflict because Gonzalez and Gonzales-Garcia are 2 different names.

In South America, we have 4 names: First name, middle name, father's last name and mother's last name. i know most of the time INS would put your four names on the green card. Lets say her name is Mary Ana Gonzales Garcia. In the card the name shown is Mary Ana Gonzales-Garcia.
First I thought that is not a big deal then we went to the SS office and they put the name just like the resident card.

Answer 1

I am not sure how that would work.. Maybe she should talk to the social security office.
I would think if her legal name (birth certificates) is Gonzales Garcia (no dash) then she should use that for everything.
Usually when a dash is in a name it is assumed to be a married woman using both her maiden and married name(which is not the case with your wife)
I am not sure if there is a dash where there should not be , or isn't one where there should be by your question.. But whichever is correct should be the one on the card and she should go to the SS office and have a new card with the correct name and spelling listed. Just explain to them the problem and ask for advice. Better safe than sorry.
Most likely it won't be a problem with checking accounts, credit cards, things like that. But it could be a problem with things like drivers license, taxes, any legal issues.
Good Luck!

Answer 2

my cousin also had the same problem (he is from PR) and uses, for example, juan diaz instead of juan carlos diaz garcia, and it has never been a problem with the bank, or credit cards, or bills, etc. i think it should be fine.