L2 for wife - EAD and Marriage Cert questions

[jais123]

I am currently in US in L1B. My wife is applying for L2 from Delhi. She got new passport with my name under "spouse" and her "post marriage" name on the passport.

My name : AAA BBB
Wife's maiden name: CCC DDD
Wife's name in new passport (changed after marriage- my surname added): CCC BBB

1. Our marriage certificate holds my name + her "Maiden Name".
- Will the marriage certificate work fine?
She has filled DS-160 with post-marriage name but under one f the section on DS-160 she mentioned her "maiden name" where it was asked (there is a section in DS-160 which asks to enter maiden/old names)..

2. Can she apply for EAD right after ariiving in USA? I know SSN will take 3-4 weeks but do we have to wait for SSN before applying for EAD?

[txh1b]

1. Everything seems fine. No issues
2. EAD can be applied without SSN.