C, E, G and A. Yes, that works as well. You're right, there's no D to serve as the fifth, but we've seen notes dropped out of chords before. The point is that a big part of what a chord is named depends on what it is being used for. You may not know it, but context is a vital part of any chord. I've told you before but it really needs repeating.
Music is motion.
Melodies and chord progressions move from one point to another and that movement helps us to define matters. Musicians and songwriters should be constantly aware of the purpose of a chord pattern, of the function that a particular chord can serve in a song. This will include using them in songwriting exercises as well as looking at how they have been used in the past by other songwriters. Both articles are available to you right here at the Online Guitar College. I would also recommend that, in your spare time, you pick a chord, any chord, and write out its component notes.