There is a big difference between a name mismatch because someone has misspelled their name by a letter or two, and a name mismatch because you have used a completely fabricated name that does not resemble your own name in any way. In the case of the latter, I'd be very surprised if Bittrex changed the name on the account for you, since there will be no proof the account actually belongs to you and hasn't be hacked or stolen from someone else. The only way to know is to contact their support.

Having said all that, is it worth it? Exchanges are notoriously poor at keeping KYC documents safe and secure. Even the biggest exchanges aren't trustworthy in this regard. Binance was hacked for thousands of users' KYC documents, and Coinbase were actively selling client data to third parties. You'll have to decide whether or not it is worth it for you, but I wouldn't be sending my documents to a faceless stranger at a company with unknown security practices for $150.