Questions previously made anonymous could stay anon but any new posts from this point on could not be anonymous.
Most Helpful Guy
It wouldn't affect me personally because I never use the anonymous function.
Generally speaking I think it should be kept. Yes, there will be trolls and whatever - but seriously trolls are trolls. If your self-esteem is this fragile you probably shouldn't be on the internet to begin with.
On the other hand anonity makes it possible for people to answer on things they normally wuold avoid answering to. Controversial opinions which everyone has the right to state, sexual things they might be ashamed of, asking questions which could possible come out if they weren't anonym, etc.1
Most Helpful Girl
I like the anonymous feature for people who have had harassment issues on the site or want to protect their privacy. I don't like it for people who use it to troll and harass people.
I wouldn't care for myself though. I so rarely use it there'd be no change.1