There is some logic in the upper and lower frequencies of the bands, however. The "3x10^n" frequencies derive from wavelength in meters. Recalling that the speed of light in air is 300,000 km/s, that means a 1 meter wavelength translates to a frequency of 300 MHz, 10 meters is 30 MHz, 100 meters is 3 MHz, etc.
At some point, some wise soul decided that it was time to start over at a single digit for L-band at 1 GHz. The new regions are in octaves, except for 3 GHz, up to 8 GHz. If anyone knows why 12.5, 18, and 26.5 GHz band edges were chosen, I would appreciate your letting me know.
Regarding the Ku, K, and Ka bands, supposedly K was named after the German word for "short," as in shortwave - Kurz. Ku is supposedly for K-under and Ka is supposedly K-above. That, of course, is inconsistent since since the K, if is derives from Kurz in wavelength, so K-under would be a lower (lesser) wavelength (hence higher frequency) and K-above would be a longer (greater) wavelength (hence lower frequency). Mostly likely, the certain origins are buried with their progenitors.
This chart shows the relative positions of the most common frequency bands, and is not to scale.