HUD can be disabled and restored by typing tm into the console, but the command disables the entire interface, including menus. A hotkey would also be more convenient.
Most likely not possible within the game, but there may be a suitable mod available.

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2 Answers

Install Menu and Camera Toggler mod — HUD toggle is mapped to the H key by default and disabling doesn't turn off the UI elements, unlike the tm command. Flying Camera Mod is a potential alternative.

source (retrieved the tesnexus.com pages with Wayback Machine)

Use BTMod 2.2. From a reply on no HUD (a different mod):

Open the prefabs/menu/hud_mainmenu.xml file with notepad, and each time there's a number with alpha in the line, you replace it with 0.

It'll make every single element invisible like typing tm in the console, except you can still talk to people, loot and otherwise play as if the hud is turned on.

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