It is named Aeolian dominant because its sound derives from having a dominant seventh chord on the tonic in the context of what is otherwise the Aeolian mode.
It corresponds to Raga Charukeshi in Indian Classical music.
This scale can also be obtained by raising the third degree of the natural minor scale or lowering the sixth degree of the mixolydian scale.
The name melodic major refers to the combined scale that proceeds as natural major ascending and as Aeolian dominant descending.
It is named melodic major because it closes the augmented second in the harmonic major scale by either sharpening the sixth (ascending) or flattening the seventh (descending).