All these settings are on the Settings → Public profile page.

Who can see your profile?

Everyone: your profile is also open to visitors who are not signed in.
Only signed-in members: only people with an account can see your profile.
Only me: only you and the members whose follow request you accepted can see your profile.

You can hide the sections of your profile (statistics, achievements, activity, games, words, exam date, follow lists, questions) one by one.

How is your name shown?

If "Show my full name everywhere" is on, other members see your first and last name ("Ayşe Yılmaz"). If it is off, only the first letter of your last name is shown ("Ayşe Y."). The preview on the settings page shows how other members will see you.

This setting does not change your username. Your username appears in your profile address, in comments and in lists. If it was created from your first and last name when you registered and you don't want your last name to be shown at all, change your username too.

Profile photo

You can change your profile photo in two places: with the camera icon at the bottom corner of your photo on your profile, or on Settings → Photo & account. After you pick a photo, a window opens: drag it into place, zoom or turn it; the part inside the circle is what others see, and the preview shows the result. A photo can be up to 10 MB.

Photos you replace or remove are kept in Your earlier photos (the latest 12). Tap one to use it again, or delete it for good with the cross at its corner. Photos you replaced also show on your profile: when someone taps your photo, they appear as small photos along the lower edge of the big one. Photos you removed are not shown on your profile; they stay only in this list. If you delete your account, they are all deleted.

Blocking a member

You block a member with "Block" on their profile. A member you block:

cannot see your profile, follow you or ask you questions;
cannot reply to your comments or challenge you;
is not told that they have been blocked.

When you block someone, the follows between you, pending follow requests and unanswered profile questions are deleted; open challenges between you are cancelled. The list of members you blocked and the "Unblock" option are in the Blocked members section of the Public profile page.