How would I go about tagging a character's own name so that it will be categorized under characters, but not set apart from others with the same name using _(character). For example, a character named James vs James_(character) will elicit totally different search results yet both will be labeled under Characters

Change the tag's type from the "Tags" page.
If it's a common name, you can replace "character" with the owner's name. For example, "name_(justjack)".