Why not make your new bittrex account and made the same as your pasport if you can be still manage your account and transfer the funds from your bittrex account just transfer it to a new account verified. And only support can help you out with your issue better to wait for their reply and tell the story why you are not put your real full name and tell them for security purposes only and you didn't know that they will ask for passport..
But i feel that it won't work beucase they are always asking for proof.. There are lots of people who are experience of security issue with bittrex
Just like this thread
https://bitcointalk.org/index.php?topic=2279977.0Because @OP indeed might not be able to move his/her funds out, depending on what level the account currently is.
Alot of people ( from EU countries aswell, including me) recently got their accounts disabled, and i'm not sure how one would regain access to withdrawing the funds if you can't verify your account.
The "New" Status on Bittrex currently allows for an astonishing withdraw limit of ......... 0$! a day..