EAD name different than SS name... Which to use for E-Verify?

[cobrakid 22]

Hello Folks,

Here is the backstory: my wife (Canadian) got her social security card shortly after we got married. It was in her maiden name. She then went back and changed it to her married name. However, once the card arrived it had her middle name combined with her first name (ex: Jenniferchristine). We went back to SS offices to try and get this changed, they tried but were unable to, saying USCIS / Dept. of Homeland Security has a "lock" on it and it cannot be changed until after we receive her GC - they related it to a mistake by an officer at our POE. Unfortunately, in that area, we are a dreaded interview wavier case, so who knows when we will get that.

Shortly thereafter, her EAD arrives. It has been correctly listed as ex: Jennifer C (reflecting our AOS forms).

Here is the issue. She now has a job. She has to fill out an 1-9, a W-4, etc. So which name should she use on those forms (which will then be used in E-Verify)... the one attached to her social security card or to her EAD/AOS?

I have tried the E-Verify self check, but that is no help on any of her "names" since she doesn't have any credit history or anything, so there is not enough to self check her. I've tried contacting all the different agencies and just get spun in circles, as always. So I'm going to try here!

What do you guys think? Anyone gone through this?