Learn English – A word that describes something that has been given a name

Is there a word besides named that describes something that has been given a proper name?

For example, a guitar is just a guitar, but if I call it, say, Shirley, is there another word that would now describe the guitar?

I'm looking for something specifically that can be used to identify things that have names (like people) but could also include books and movies, or say "Old Glory" for the flag.

Is there such a word?

EDIT: Here's a bit more information:

I'm looking specifically for a noun, a word which describes any object, person, or idea that has a name.

Perhaps an example will help: say you had a hat full of names, movie and book titles, as well as say names of famous characters from tv shows, and maybe even important events in history like "The Great Depression".

If I asked you to reach in and pick one, what could I say to pick besides "choose a name" (and of course, besides "choose a piece of paper"!) that would describe every one of the items in the hat?

EDIT2:
Okay here's some final context for everyone. The reason I posed this question is I am developing a game for windows phone that involves guessing a name, but although "Name" is a simple enough name for the object, it also has additional properties like "category" and "description".

So if I called the object "Name", I need an additional property to reference the actual name of the object. If I used "Name" again I would be accessing it via Name.Name, and that's just silly.

In truth, this isn't a big deal, I ended up using "Name" as the object, and "Title" as the name. This was more a "curiousity" thing, where I wondered if there was a way to accurately name the object, so I could keep "Name" as a property.

Ultimately, my favorite solution is to keep the "Name" as the object and "Moniker" as the name. This feels like the most intuitive way to do it, but I'll probably keep it as it is with "Title". But since that's my favorite that gets the answer, thanks to all who contributed!