The name was previously used for other train services, and a funny fact is that the old Hayabusa train was going... in the exact opposite direction, to Kagoshima.
The reason for the selection of this particular name was that the peregrine falcon reaches a maximum speed of 320 km/h, a speed that coincides with the maximum speed of this Shinkansen line, for now the highest commercial speed in Japan.
EXIF info:
Nikon Df
Lens: 24-70mm F/2.8G
Focal Length: 24mm
Aperture: F/5.6
Shutter Speed: 1/250s
ISO Sensitivity: ISO 2000