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Youll need to open a ticket with their support and query the exact procedure and time it would take to clear your situation. Other people have undergone a similar situation using either fake or mismatched names with varying experience as can be seen here:
Bittrex : Name Mismatch.
"Name Mismatch" is a very famous error happened to Bittrex's KYC in late 2017 and it's a totally different case. At that time, Bittrex was still among top exchanges and very picky with KYC. They even closed for new registration for some times. Every small difference, even a dot or a comma was deemed "Name Mismatch". But then when Binance showed up and attracted users for its low fee, Bittrex saw the threat and loosely approved all the undone KYCs. My account was a typical "Name Mismatch" victim but then approved without any of my effort.