If you want to anonymize your Bitcoin, then just sending all of them to another wallet of yours is not very safe. You should use a mixing service. They will make it more difficult to trace the Bitcoin.
My other wallet no one knows which one I have, yes they can see in blockchain.info where the btc has gone, but that does not confirm that the wallet is mine.
But yeah a mixing service would be great, still I think the guy that sent me the BTC used 6 different wallets to send the amount to me, so he has dissappeared by now.