Yes! Also, all the WishLists under your profile will have the same privacy setting. Click the pencil icon under your profile picture, then select “Edit Profile Info”, then select the privacy you want:
Public - anyone can see your profile and its WishLists Friends - only your friends can see your profile and its WishLists (once you accept their friend request) With Link - only people to whom you send the link can see your profile and its WishLists. Your profile won’t show up in any search results. Private - only you can see your profile, and its WishLists (no one else)
You can determine who can see your profile for every profile you create.