Go to Settings → Account. If the option is not there, the administrator has turned name changes off, or you have used yours recently and there is a wait before the next one.
🚨 Your old name is held for a while after you change it. That is not the site being awkward — a name that becomes available the instant you drop it can be taken by somebody else, and everything you ever posted under it now looks like theirs.
Posts you have already written keep showing your current name, because they are attached to your account rather than to the text of your name.