TL;DR: it should often be labelled as Dm6/B.
How to label a chord... In discussions around questions like this, there seem to be implied assumptions like the following:
- (1) for any combination of notes, there exists one way to label it as a chord symbol that's "correct" for all intents and purposes in all imaginable contexts
- (2) chord symbols in songs should be understood as some kind of harmonic analysis
- (3) the chord's root note is the be-all and end-all "this changes everything" factor in harmonic meaning
- (4) in order to know the one-and-only correct functional role and perspective for a chord, you need to identify the one-and-only correct chord symbol label.
I disagree on all of those points, and "Bm7-5" in particular is a prime example. In many cases, instead of Bm7-5 what should really be written is Dm6/B, or even Dm/B or simply Dm. When the chord is used in a simple Am - Dm - E7 - Am song as a fancier Dm, writing "Bm7-5" badly obfuscates the fact that it's doing the job of a Dm. Many players might not even know what the "7" is, let alone the "-5" (sometimes even written in small letters), which is IMO often the most important note in the chord. So they play "Bm" or "Bm7" - with the F# note and all. I know naturally musical people who don't know theory, but can accompany songs by ear, and when hearing this "Bm7-5" chord in a song, they'll play a Dm - which is what the chord really does.
If you write lead sheets for amateur musicians, please stop the "Bm7♭5" nonsense and leave that for theory snobs and more advanced audiences.
Chords are not monolithic objects, even though the practice of using chord symbols might lead you to that conclusion. There's no half-diminished chord receptor in your brain, which would activate only upon hearing a half-diminished chord. Chords consist of separate notes, and each of them can have its own role in the harmonic story. The bass note is not necessarily the most important note in affecting where the harmony seems to turn. Take a song that's in Am and has this "Bm7-5" chord written in it. If you were writing an arrangement of the song for, say, two horns, and if you had to choose just one note from B-D-F-A for a harmony voice, to deliver a barebones version of essentially the same harmonic feeling, which note would you select? Self-evidently the bass note because it changes everything? YMMV, but as a first choice, I'd select either F or D. What if it was a B7 chord? Then the obvious first choice would be D#, not B.
By the way, Thelonius Monk called it "minor six with the six in the bass".