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What We Already Know
From this we can deduce that Kuroyukihime's first name begins with 'Sa'. Examples would be Sachi, Sachiko, Satsuki and Satori.
We also know that at the end of episode 5, Kuroyukihime says that her real name is similar to her nickname (reffering to 'Kuroyukihime').
Because 'Sa' doesn't appear in 'Kuroyukihime', we know that it's her last name that is similar to 'Kuroyukihime'. For example, her last name could be or could include (or could be similar to) Kuro or Yuki.
This isn't just guess as it ties in with what we already know. Asuna's real name is Yuuki Asuna. This goes back to the fact that we know Kuroyukihime's last name is related to her nickname. Yuuki (Asuna's last name) is really similar to the 'yuki' contained in 'Kuroyukihime'. If Kuroyukihime is the daughter of Kirito and Asuna. We could probably say that her last name is Yuuki.
Another reason for Kuroyukihime being Kirito and Asuna's daughter, is the fact that she resembles Yui. Someone who Kirito and Asuna treated and loved like a daughter. This is not a valid reason as someone you treat like a daughter, won't look like your actual daughter, obviously. It is just a correlation.
We can very much assume that Kuroyukihime's first name is Sachi. This is because Sachi is someone who Kirito cared for, and lost. We can speculate that Kirito might have named his daughter after someone very important in his life, as a lot of people do. We know that Sachi was who Kirito chose because, going back to what we know, Kuroyukihime was addressed as 'Sa-Chan'.
Most Likely Name
From all of this information and speculation we can assume that Kuroyukihime's real name is:
Most of this page is just speculation and guessing.
Everything speculated on this page could be totally false.
I am not saying any of this is fact, I am merely using information I have access to as a means to speculate the what the unknown could be.