Name a chord from its notes
2 names fit
Candidates are ordered by: the root being the lowest note you gave, then the root being spelled the way you spelled it, then the simpler chord type in the order this site lists them, then the root that needs fewer accidentals. Nothing is dropped — every chord whose notes are exactly the notes you entered is here, and where two names fit, both are right.
Why there is more than one answer
C, E, G and A are four notes. Read from the C they are a major triad with a sixth added — a C6. Read from the A they are a minor triad with a seventh on top — an Am7. Nothing in the four notes decides between them, and any tool that shows one name has made a choice it did not tell you about.
So this one prints every chord in its catalogue whose notes are exactly the notes you gave, and the rule that ordered them is printed under the list. That rule is the whole editorial position of the page: the order is a convenience, not a verdict.
The spelling matters too, and it is kept. Type C E♭ G♭ B♭♭ and you get a diminished seventh with its double flat intact; type the same sounds as C D♯ F♯ A and you get told something different, because they are different notation.
Questions
Why does one set of notes get more than one name?
Because a name is not a property of the notes. C, E, G and A are a C6 and an Am7, and which one is right depends on what is in the bass and what came before — neither of which is in the notes. A site that prints one name is choosing for you without saying so.
Does the order I type them in matter?
Only for the ordering. The first note you type is treated as the bass, which moves the names whose root is that note to the top and gives the others a slash name. The set of answers is the same either way.
Why is a chord I know missing?
Because this site has 22 chord types and the notes you gave match none of them exactly. It does not guess at chords with notes left out: an answer that required assuming a missing fifth would be a different question, and a less honest one.
Does what I type leave my browser?
No. The whole search runs in the page. There is no request to make and nothing to log.