At the start of the series L hides behind a computer screen which draws criticism by members of the Japanese Police who were assigned to track down Kira.
while in the context of the Kira Investigation in how the Death Note works and L's correct reasoning that Kira needed a face and name, hiding his face initially is a good defense against the Death Note.
When she was saying about how she met L, Naomi Misora said she worked under L by taking orders from a computer screen. this sounds just like how L was working at the start of the Kira Investigation and since the BB Murder Cases (which L comments is where he remember Naomi from when told she was missing) had nothing to do with the Death Note this means he was hiding his face not as a defense against Kira.
So why was L hiding his face before taking on the Kira Investigation?