Sort of. Fictional character names are just words... unless these words are used in trade, at which point they become trademarks.

And in this context: "Sauron" is a registered trademark. https://trademarks.justia.com/772/04/sauron-77204394.html

This status doesn't necessarily give the owner absolute control of the mark, but it can limit the ways in which others use it in trade.

Things would be this way whether "Sauron" was ever the name of a fictional character or not. The use as a character name by the trademark owner neither implicitly enhances nor diminishes the trademark's integrity.