Now, if you'd wanted privacy, there were a lot of ways to do it. You could have established an LLC or a land trust, and purchased it in the name of the LLC or land trust. You'd still have had to personally guarantee the loan, but then the trax records would show that "Upper East Side Condo LLC" had purchased the property or, similarly, that "Upper Least Side Condo Land Trust" had done so. Your name wouldn't have been visible.
At this point, you can still establish a land trust or an LLC and transfer your property into it. At this point, the records still will show your purchase from the previous owner. However, it then will show a transfer from you to an LLC or land trust. And no one can be sure that it's controlled by you. That's done frequently for privacy and asset protection. You might also consider establishing a living trust (of which a land trust is a variation), and moving your property into the living trust. That can be a good estate planning tool. I'm not a lawyer or financial planner, so this isn't legal or financial planning advice. However, you should contact a lawyer with expertise in estate planning and get some input. That can also provide some privacy.
Hope that helps.