Let's try RAZANUR TUK, aka Pippin. It includes 'Rana' (a name of the Moon) and two Us ('possessed U twice'), so all we need is to find a deer and publicity in... ZRTK.
...
Maybe not?
Frodo is also given the name 'Daur' on the Field of Cormallen, which at least starts with a D(eer), but unless there's some sneaky subtraction in the clue, I can't see it.
hS
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