nope. you will need your advanced parole for this purpose. but if it is not yet approved(485) then you can simply use your H1b.
you are on the verge, so best of luck to you. Dont forget to carry our AP! i dont think that the name problem is that big a deal.
if you do get approved then you will use your AP,
if they do notice,
and if they ask you about it, then you can just explain it away as a mistake. its not like they are going to stop you from entering a country due to data entry error.
there are a lot of if's in that statement and so i think its an ok bet.