Unless you need to hide your face in the public for personal security reasons, you should always have a professional looking photo represent you. You might be able to get around not having a photo, but as studies show in having photos in Google search results, those with photos might expect a significant increase in CTR (click-through rate) after people find you in LinkedIn search results. Actually, LinkedIn themselves have said that profiles with photos are 7x more likely to be viewed by others. And, besides, if you want to make a deeper connection with someone,shouldn’t you be showing your real face?