What would you call this chord?

[datroof]

Pedro.

[Forgotten]

Pedro.

I would vote for Pedro...

[datroof]

What's the context of the chord? What chords come before and after this? That might give us some insight into its function.

[xtp]

I tried it out in a couple of inversions, but it always sounded A-ish to me, not B-ish, probably because of the strong [a] minor third interval. I would probably agree with Jafo,

Or an Am/B (possibly an Am9)

and call it a Am9 [omitting the 5th and m7th] or an Am with a B in the bass.

[zyzygis]

Now you are all just being silly!
Anyone who understands music can tell you that this is a female chord and should be called Hellen or Carol.

[jancivil]

With no actual music this happens in, no context, there isn't really a tertial chord anyone can call.

In and of itself, you have A, B, & C, which as a vertical sonority is secondal.

I would note that the sixth you describe, C w. A above is 2/3rds of an A minor; so, if you typically tend to work in chords made of thirds chances aren't bad that an Am with a B bass happens. If so, should you need to convey it by a name, 'Am add2' will suffice (cf., add9, you know).

There is no sound basis for a tertial harmony built on a B root w. no 3 (nor a 5), but nobody knows from what we have at this point.

[Mushy Mushy]

Jan!!!!

[jancivil]

hiya

[Mushy Mushy]

hiya

We missed you.

[jancivil]

thanks for that

[delahlin]

Edit: and just for clarification, an implied 5th (F#) is fine because it doesn't change the character of the chord either way.

It's ambiguous. See if B7b9 or B7alt (b9, b13 and/or b5) works for you.

By its ambiguous are saying that there is no well defined name for such a chord?

No, I'm saying there is more than one possibility. How does adding an E sound to you? That could suggest/imply B7b9sus, Ami/B, C6/B, CMa7/B, etc. If F sounds good to you, that could suggest F/B, and so forth. (In other words, the 4th and 5th notes you choose to add will remove much ambiguity).

Also worth noting, ambiguity is not necessarily a bad thing at all. It's a quality you can take advantage of.

I know this is old, but thought I'd respond. Fantastic answer by @datroof (in response to a great question). I struggled with naming this exact chord in my early days. I finally settled on B7b9sus. FYI, the 3rd of this chord is not necessarily "implied," like you might think, the same way it's not implied in Herbie Hancock's entire "Maiden Voyage" masterpiece. It's "ambiguous" (and also extremely cool) when the suspension, or whatever you choose to call it, is not resolved (although it's also a nice dissonant to easily resolve the suspension to an already dissonant B7b9 -and that way you can have both the E & F!). Great question!

[jancivil]

Maiden Voyage isn't implying thirds because the harmonies are quartal.
B7 something something is tertial, which means it has a third or something in its place (some kind of E or C in the place of its D).

You don't have to name it. What was given is B, a C either an octave and a minor 9 or a minor 9 above it, and an A
By itself, again there's no there, there to base a name in; except a sonority or chord if you must, by seconds. It's actually a thing, just like the Maiden Voyage is fourths. I'm saying there may well not be a well-defined name for it. If I hear it, I may be able to place it. It could be an A minor add 2, which by an Occam's Razor kind of assessment has fewer assumptions to fill in with than a B7 anything if we are naming by thirds. A to C is our third, & to be a full Am add2 we're only omitting a P5 which is actually done all the time in both guitar and piano arrangements. But without hearing it it's unknown to us all and this is just words.

[TribeOfHǫfuð]

If A is root, I bet on Jan, but note the omitted 5th in that case. Maybe it is the fifth, invertet and jumping down and up and sideways because its arse is on fire. It is not a scary passing movement in natural minor as long as you do not stay there too long.

[jancivil]

being that a perfect fifth is absolutely the first thing to lose, by_far the simplest guess is Am add2, but again, it doesn't have to be anything and doesn't even have to have a root; we don't have any music to tell us it is or isn't any of the things.
To begin with, the OP doesn't like 'no third' in the chord name which is just reasonable.

[TribeOfHǫfuð]

True. Without context or at least a root, we have a persistent problem. Tho, I do recall a few chord questions of the sort without context and have seen many creative and ambigious namings. Just another reason for me to cling to the terms of counterpoint in which it could be a lower voice on it way back to tonic by steps or skips, next thing it will land there (a) while a and c moves a third upward In steps or skips to c and e, and we have the complete triad. Harmonies like the “chord” in questions have their place and time in counterpoint too, if not for anything else, then a brief step in movements.