It is unlikely to be Virgin's security checks. Chances are your name is on the TSA watchlist (assuming you are travelling to the States) It has happened to me so I can sympathise! After years of travelling with no problems I was stopped from using online check in twicce and checking in at both ends involved hushed phone calls by the agent. Virgin have told me to contact TRIP
http://www.dhs.gov/files/programs/gc_1169676919316.shtm to try and get my details added as being OK (they don't remove names, just add details of people that they aren't looking for if that makes sense??) Be warned that my last trip I was stopped from boarding and taken for extra security checks so be prepared!
PS I don't have a common name and have never been involved in terrorist activities!!!!