Name of "the" benzodiazepine
Let's look at the „[1,4]diazepine“ part more closely. (Standalone, it's correctly named 1,4-diazepine.) The „-epine“ in the Hantszch-Widman system stands for unsaturated seven-membered ring. More precisely, one with the maximum number of noncumulative double bonds. (IUPAC uses that term instead of „conjugated“ probably to avoid confusion with physical electronic conjugation, which might not be the case, as we're at the level of topology, not even geometry.)

The exact structure is specified with indicated hydrogen. There are four 1,4-diazepine structures, 1H-1,4-diazepine, 2H-1,4-diazepine, 5H-1,4-diazepine, and 6H-1,4-diazepine (not considering their stability/existence in tautomeric pair/multiple):

  

In the world of abstract organic chemistry nomenclature, 1,4-diazepine without indicated hydrogen can be represented as following structure (dotted bonds for unknown bond order, any arrangement of noncumulative dbl. bonds assumed; no explicit hydrogens):



When fusing with benzene, 1,4-diazepine part has to be numbered as follows (not the other way), to get lowest numbers/letters when starting with heteroatom:



… obtaining benzo[e][1,4]diazepine (new numbering of the resulting structure marked, partially; coincidentally we get the same set of numbers for nitrogens):



Indicate the hydrogen to get our 1H-benzo[e][1,4]diazepine:



(But note that fused ring nomenclature is quite long and complicated, generally the final numbering could also depend on the indicated hydrogen position.)

Finally, note that the new nomenclature has simplified the names of benzo-fused rings, the current preferred name is 1H-1,4-benzodiazepine.