ok, I'm working on progressions. I arrive at this chord in STD tuning

mute low E
1st finger on A 2nd fret
3rd finger on D 3rd fret
2nd finger on G 2nd fret
4th finger on B 3rd fret
mute High E

So my question. After consulting several chord web sites, I seem to be perplexed. The only sites give this chord name as F6/B or Dm6. Why doesn't this chord have a B name? If it does have a B name, then what the heck is it?

OK anyhooo

Thanks