Song Help Request which chord, based on stack of notes?

Received sheet music.
There are 2 notes (stacked) at each point on the staff.
Above some of these, friend has written in chords.

Where there is a C and a G, she's written in a C chord.
...a B and D, a G chord.

I can't find the pattern, though, to fill in the others.

On my Circle of 5ths cut-out, I can see that a C chord is made up of a C, E, and G, and that a G chord is made up of GBD. So I can see where she got the chords mentioned.

For the notes D&G, would it be a G chord?
For the notes C&A, would it be an F chord?

i.e., I just find which chord on the Circle includes the two notes (regardless of I, IV, V) and use the associated chord?

If so, then what do I do when the notes are C&D?

I do get the idea, thanks, ubulele! I had no idea. Very helpful

Since there's no simple formula, I'll ask the friend what she wants played in the additional spots.

I enjoy even finding out where there's more to it, so this is great!

I will play with this... Thank you, Bill1!

I had a transcription gig where I was given a few melodies, and asked to figure out the chords to go along with it. For some I was able to find recordings to reference, some I couldn't find a thing. I recall giving the client a couple of options - as in, "here's one simple set of chords, here's another that sounds jazzier and more interesting but is a bit harder to play." So it comes down to (1) what chords fit in the key, and (2) where there are a couple of choices possible, what kind of sound you like.

You may run into situations where the notes given omit the tonic, or root note. What does that mean? If you use your ear to figure out what the root note is (E in an Em, C in a C major, etc) then you'll have more information when it comes to constructing chords. For example, in the key of C, if you're given a C and an E, that can be an Am or a C chord (or an Fmaj7) depending on the root note. It gets a little more complicated when you have a bass note that's *not* the root of the chord. (This is more common on guitar than uke, where you have more bass notes available, so you see a lot of G/B - G with a B in the bass, or C/E - C with an E in the bass.)

I hope this helps!