Hi, Deadman and all.
Generally, you should use the name of a character to clarify identities where they might otherwise be confused. Remember, unlike a [visual production of any kind,] your reader only has your writing to help them picture the scene.
As for how you address the character’s identity “outside of quotation marks,” you should generally stick to a single unambiguous name for the character in third-person perfect or unidentified third-person imperfect. In identified third person imperfect or first person, your labeling of a particular character is that supplied by your “viewpoint” character. As a rule, you must be consistent in third-person perfect, and you should be consistent in other tenses. However, deliberate changes can indicate changes in opinion by the viewpoint character or observer.
Inside of quotation marks, the character themselves will govern how the particular character is identified or addressed.
Cheers!