Because they're different people, she and he would still remember the names of their Syaoran and Sakura, respectively, but they wouldn't recognize those as their names! However, considering the circumstances (Oh, Clamp canons...), it's likely they'd be among the first to be able to regain their names.

We'll leave it up to your and the Syaoran player's discretion, so long as it's after at least a month of gameplay!