Urgent - Query regarding documents for US

my name has been picked up in lottery for H1b this year and i have some query regarding documents name variance.
I have Full name in Passport < FN LN> and in official documents , however in all other documents like Marriage certificate, Birth certificate and educational certificates its First name only , no last name is there in any other document.
Will there be any issue while applying for SSN or bank account or any other area will create this issue? Please suggest.