It stays on after logging off :). Logging screen has CosmosBird elements and logging into different character, with different skin, also shows some CosmosBird elements.
Some of elements of the UI do persist when logging out to the character select screen. That is working as intended by the game. Some elements lingering over onto other characters, after you have done so. That is a bug that would have to be fixed by the game's developers. As a UI Skinner, I don't have control over such things unfortunately.