Indian passport renewal with maiden to married name change


I am going to renew my Indian passport at San Fransisco Indian embassy and I also want to change my name in the passport from maiden to married. I will traveling to India for H1B stamping after that but the issue is that the I797 and I94 would have my maiden name. Will this be a problem during H1B stamping ? Currently, I have ‘LNU’ (last name unknown) as my last name in I797 and I94 and my passport has no last name (it is left empty). I would really like to add my husbands’s surname to my last name in the new passport.