Only list owners can see the information you enter when joining their lists. Depending if the list is Public or Private, your username might show in the Members tabs of lists you join.
If the list is public, the top 10 usernames will be shown on the "Members" tab. If you are in the top 10 and are logged in, you'll see a badge next to your username making it easy to find your spot. If you're out of the top 10 and want to see your spot without logging in see this article.
If the list is private, no one can publically see usernames. Only a logged in list owner can see all usernames in their Manage tab. Logged in list members will be able to see their position while logged into their Dashboard or by entering their email or username into the check position popup.