If you have an unfilled limit order which is resting on the book at a stock exchange, anyone with L2 data (available for single-digit dollars per month from InteractiveBrokers, among others) will be able to see it, though it won't be linked to you.
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 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.