By doing this, only Binance will know where you have transferred your dogecoins or any other cryptos that you will withdraw from them. I understand that you're trying to improve and increase your privacy from anybody or even from them. You don't have to worry about that if your funds are clean and it didn't come from anything illegal or unclean. Also, if it's not that much to think of, there's nothing to worry with. Another option for you to increase your anonymity, you can simply convert it afterwards into a privacy coin but you'll have to use an exchange that supports it because Binance isn't or some instant exchange like exch.