I know we discussed this awhile back when the dev. team was looking into it, as well as taking in player feedback for what they’d like to toggle, but we finally got an update on the situation! The following options are aimed at implementation in patch 1.21.

The ON/OFF display feature won’t only apply to your own name. You will be able to set ON/OFF values for displaying each of the following categories:
  • Your own character
    • Name/Icon
    • HP Bar
  • Party Members
    • Name/Icon
    • HP Bar
  • Other Players
    • Name/Icon
    • HP Bar
  • NPC
    • Name/Icon
  • Enemies
    • Name
    • HP Bar
    • Level
    • Enemy Icon
    • Enmity

It’s currently not possible to toggle the linkshell and bazaar icons independent of your name in this feature (for example, leave name displayed, but hide linkshell/bazaar). We will look into including this functionality in version 2.0.