While using one name does make it easy for snooping/cranks, it also really narrows down who's doing the snooping, since tracking is a two-way street. Also, if a company is going to decide whether to hire you based on a social media site like facebook (barring pictures of drug use and/or illegal activity) as opposed to whether or not you're qualified for the job and could meet the job requirements, then they're not a company worth working for.
The other red flag is if they ask for any account passwords that are not created by and/or directly controlled by the company itself. This is a violation of privacy, and should be treated as such. The only time you are required by law to disclose such information is when an attorney is present, or if you're required by a court of law to do so. At any other time, you're free to laugh at them and leave. At least that's how it works in the U.S., it might be different in other countries.