>> My fear is if I am accepted but choose to stay, but my name is listed on the YC website
I don't know who you work for, but frankly it sounds to me like you're over-thinking this.
You're suggesting that BigCo routinely searches the YC website, or perhaps the whole web, and then name-matches that against an internal list of employees? I guess maybe they do, but as an employer this sounds bonkers. Quite apart from names not being unique, it sounds like a colossal waste of time. Why stop at YC? I should do this for all incubators...
Plus, they're gonna fire you preemptively? For looking elsewhere? Geez man, what kind of place are you working for?