Job listings are public information, your resume may also be considered public info if you have sent it out to recruiters or public job posting sites.
Listings you've applied to could be potentially private. But if you use an alias (and only reveal your real name after the company agrees to interview you), then it's not a problem either!
i use an alias on stackoverflow, and i use an alias here on HN!
My google profile is also an alias. My facebook profile is also an alias. My twitter, same. And if i had a linked-in profile, it would be an alias too. Some of those alias may be the same, but some i deliberately make different, so that i can choose whether others can associate different aliases together as the same person.
Why anyone puts their real name online is beyond me. When i tell my real life friends, they are shocked, and also ask whether it's inconvenient. Yes, i would answer - it is inconvenient, but it is more control. It gives you the option to prevent others from being able to track all my activities online across different services (at least, not easily).
You replied about online usernames, but not about the question asked - do you apply to jobs using an alias / how do companies react when you change your name in the process?
Listings you've applied to could be potentially private. But if you use an alias (and only reveal your real name after the company agrees to interview you), then it's not a problem either!