Q. Do quotes need a name behind quote?

Yes -- anytime you add information to your work that's not original to you, you need some kind of attribution. This is true even when you summarize or paraphrase info, but quotes make it especially stand-out as almost a literal red flag. Citation needed here!

How to Add a Name

1. Narrative citation: Lin-Manuel Miranda sings, "I am not throwing away my shot."
   1. In this case, there had better be a citation on your Works Cited/etc. that starts off Miranda..., otherwise there needs to be a parenthetical citation still.
2. Parenthetical citation: The character of Alexander Hamilton repeats throughout the music: "I am not throwing away my shot" (Miranda).

How Not to Add a Name

If you're just quoting a reputable but otherwise generic source, you probably won't use the narrative citation. You can still quote the information/author, but leave them in the parenthetical. Being included in the narrative of your paper is a promotion, and you don't just promote "some random person" to that spot.

e.g. Seize every opportunity, and do not "throw away [your] shot" (Miranda).

Also, despite what you see in books and casually-written articles, you don't want to just plop in a epigraph flavor quote, like starting your paper off with:

"I am not throwing away my shot." - Lin-Manuel Miranda as Alexander Hamilton

That's a matter of style and tone rather than plagiarism/attribution, however.

What if I'm quoting a general saying?

Let's say you're reminding your reader not to "count their chickens before they hatch." The quotes show off that we're cribbing a phrase from somewhere but there's not any one person we can really credit with that saying. In this case, no, we won't be adding a name -- and in that particular case, it's probably not worth putting in quotes at all (and, as well, that expression may be too casual to include in a formal paper in the first place!).

None of these examples help me!

Sorry about that -- there's a lot of nuance that goes into writing clearly. You can send your paper (or an excerpt with your quoted material) to the librarians or the Writing Lab for an individual consult.