Trivia: This film got an amusing shout out at the 2006 Tribute to Bruce Willis. Specifically, the event was hosted by Alan Rickman, who was introduced as 'straight from the 30th floor of the Nakatomi building'. For added humour, Rickman then hobbled onto the stage on crutches and wearing multiple casts and braces as if he was still recovering from the injuries of his fatal drop.
Deliberate mistake: For Hans Gruber's iconic death scene, Alan Rickman's fall was filmed at high speed (for slow-motion playback) against a green screen, and the skyscraper perspective footage was added later as background. However, while Rickman falls away from the camera in slow motion, papers are fluttering around him in the background at normal speed. This was done deliberately to make the shot even more surreal.
Answer: Most large companies, particularly hi-tech or multinational ones, require visitors to check-in, especially afterhours. By having John search for Holly's name, it can be verified that he actually knows someone who works there, that there is an actual employee with that name, and otherwise assess whether John is a legitimate visitor. This scene's real purpose, however, is for plot exposition. John learns from the monitor that Holly now goes by her maiden name (Gennero) rather than her married surname. We see John's annoyed reaction to learning this, which sets up a later confrontation between him and Holly over their troubled marriage.
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