H4 EAD - name difference on passport and marriage certificate

Dear Team - could you please clarify on the below issue while applying for H4-EAD.
there is a name difference on passport and marriage certificate.
name on passport - firstn_ame last_name (spouse sur_name)
name on marriage certificate - first_name last_name (my sur_name).
while filling the name details, i need to use the name on the passport right?
And also do i need to provide copies of all my old passports too with explanation letter?
thanks for your help in advance.

Just use the name on your passport (and probably it is the same you used for applying H4). It is understood that marriage certificate will have maiden name.

No need.