wife name, SSN, and Green card don't match

[hniHnitsuJ 8]

Here are the problems with her name, SSN, and Green Card.

Her full name in Vietnamese is = Tran Thi Be Map : Tran = Last Name, Thi = Middle Name, and Be Map = First Name.

On her SSN is only shows her first and last name = Map Tran (should be Be Map, Tran)

On the top of her GC shows Map, Tran T. and on the bottom with her full name: Tran<<Map<<Thi<<Be.

My Question is should I call USCIS to get her name change? To Be-Map, T. Tran

How long will it take to have her name change, and how much does it costs?

If I am not changing her name, will this be an issue when she becoming an US Citizens in 5 years, and if she decides to sponsor her parent. Because the name on her Green Card doesn’t match with her real name in Vietnamese. Tran Thi Be Map.

If anyone run into this problem before please share your experienced with me.

Thank you for your help.

p.s. My wife wants to attend college after 1 year. We want to make sure all her name is spell correct with all the paperwork.

[txladykat 1]

Very strange that they didnt use her full name on her SSN. They always put the full name. I think I would contact the SSN office and have that corrected. I think the GC is fine if it has her middle initial and the full name at the bottom.

[hniHnitsuJ 8]

Very strange that they didnt use her full name on her SSN. They always put the full name. I think I would contact the SSN office and have that corrected. I think the GC is fine if it has her middle initial and the full name at the bottom.

I went to SSA to have her SSN name change. SSA office telling me their can not do anything, since their system is link with USCIS. Only show First, and last name only. Weird???