Bitcoin is never truly anonymous. If you buy BTC from someone/somewhere that needs ID, they know the address you buy the bitcoins to are owned by you. Blockchain.info makes no difference on that.
Thank you @DarkStar_
I will not be buying bitcoins. Somebody owes me money and will be paying via BTC and I will be using those bitcoins to pay for web hosting etc. I will be using one or two layers of anonymous VPN to login.
Then you should be safe. Your address will probably never become a target for people anyway, so you shouldn't worry about that unless the Bitcoin payment comes directly from hacked sites. Using blockchain.info and VPNs are good for staying anonymous, since only the VPN knows your IP but if you download Bitcoin core, the node that you publish the transaction to will know your IP.