I would call it an Em barre chord. The cool thing is that you can use it as a Moveable shape, which allows you to play any minor chord.
As long as you keep that shape, the intervallic pattern remains the same. [ P1, P5, P8, *m10 ]
*m10 is just a m3 played one octave higher, you can also call it flat 10 ( b10 ) if you wish.

…….......Em…….....Fm…….....Gm……....Intervals
e--------3--------4--------6--------m10------
B--------5--------6--------8--------P8--------
G--------4--------5--------7--------P5--------
D--------2--------3--------5--------P1--------
A----------------------------------------------
E----------------------------------------------


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