Search for finger pattern = {5 4 3 4 1 1}: 16 results found.
  A+add9add#9  A Augmented Add 9th Add Sharp 9th
  C#+7add7/A  C#/A Augmented 7th Add Major 7th
  F5addb5addb11addb13/A  F/A 5th Add Flat 5th Add Flat 11th Add Flat 13th
  ...

I apologize if this is obvious or well known to you, but for anyone not already familiar with it recognize that much like (and not wholly independent of) musical scales, chords are essentially defined by a predictable "formula".

E.g., every major chord is described by interval pattern 0-4-7: starting at any note, take the root, major-third (4 semi-tones above the root) and perfect-fifth (7 semi-tones above the root) and you have the major chord. For the root note C that yields C-E-G.

Rotate that pattern so that the root note is pitched above the major-third and perfect-fifth (e.g. something like 4-7-12) and you have an "inversion" of the major chord. For the root note C that's E-G-C (known as "C/E") or G-C-E (known as C/G).

Based on these interval patterns it's not hard to generate an exhaustive list of chord "families" (with members like "Major" or "Dom13Aug5" or whatever) - there are at most 4096 (=2**12) of these interval patterns in a single octave, and many of those are relatively uninteresting due to symmetry, degenerate cases or just plain dissonance. (To be fair many common chords span more than one octave.)

A given collection of notes (fret/string combos on a 6-string guitar for example) is usually going to map to some variation of one of those interval patterns, possibly with a stray interval added, dropped or repeated. (E.g., the typical X32010 fingering of C Major on guitar corresponds to C-E-G-C-E rather that "simply" C-E-G.)

So it might seem like mapping an arbitrary fingering to the corresponding chord name requires a lot of information, but it's just matching notes (or pitch classes) to a moderately small number of named interval patterns.

And it might seem like "F5addb5addb11addb13/A" is a ridiculously over-specified chord name, but that's a function of applying a set of conventional "modifiers" to a simpler/better-known/more-common chord. (In this case, `F5addb5addb11addb13` = `F5 + add(b5) + add(b11) + add(b13)`, i.e., F5 (F + C) with a diminished-5th (C), diminished-11th (B) and diminished-13th (C#) added.) You could argue that the pattern matching is trying too hard in this case, but if you're dedicated to assigning a "conventional" chord name to an arbitrary collection of notes, there's algorithmic way to do that.

Again, apologies if this is obvious to you (user Y_Y), I just thought I'd try to de-mystify it a bit for anyone to whom this seems like alchemy.

Music theory has a bunch of semi-arbitrary naming conventions that make it sound really complicated to the uninitiated, but in the abstract the chord names are basically just bit-masks that specify interval offsets from a given root note.

(By the way, I also deliberately chose something that should be excruciatingly difficult to actually play on a normal guitar.)