This is how order books work. If you don't want counterparties to see the fact that you want to buy or sell stock, your options include a) not telling a stock exchange to advertise your willingness to buy or sell stock by putting in limit orders, b) using a dark pool, or c) become more sophisticated with respect to your execution strategy, such as e.g. using repeated Immediate-or-Cancel orders, etc.
This is called Level II data and goes beyond the simple bid, ask spread of Level I. The feeds are cheap and usually free if you have enough money in your account at any traditional brokerage.