The name "Hakuda Kempo Toshu Jutsu" was chosen to reflect the earliest names of Karate systems as well as Japanese Bujutsu.

For example Gichin Funakoshi (often said to be founder of Shotokan) actually called what he taught "Rentan Goshin Karate Jutsu" or "Ryukyu Kempo Tode" the former basically meaning "self defence Karate" and the latter meaning "Okinawan method of Chinese Boxing". 

Similarly Choki Motobu called his art "Okinawa Kempo Karate Jutsu" 

We use the name "Toshu Jutsu" which is a simple alternative to "Tode Jutsu" or "Karate Jutsu" since the characters for Karate can be pronounced in any of these ways. 

Kempo is a Japanese term referring to percussive systems based on Chinese Quan Fa. 

Hakuda was a method of "Jujutsu" similar to Karate Jutsu particular to Kagoshima Prefecture (Satsuma, Nagasaki) which included some of the Ryukyu islands, aside from Okinawa. Hakuda is the forerunner of Japanese styles such as Yoshin Ryu and Yanagi Ryu. Literally it means "white hand". 

Similarly in Satsuma, southern Japan, the earliest style was called Hakugen Ryu as transmitted by the Minamoto and Hougan clans.

Kurama Yoshin Ryu's densho states that Akiyama founded Yoshin Ryu having discovered a treasure chest on mount Kurama which contained the eight scrolls of Kiichi Hogen who taught Minamoto Ryu (Hakugen Ryu) to Minamoto Yoshitsune.

But Hakuda Kempo Toshu Jutsu is just a name, often our system is simply called "Bushinkai Karate" - and that's fine too!

Above: Gichin Funakoshi (4th from left) was rarely seated next to his great rival Choki Motobu (5th from left) like on this picture. In the early days before the advent of Karate Do, both men referred to their art as "Karate Jutsu", "Tode Jutsu" or "Kempo." Funakoshi considered Motobu an uncultured thug and Motobu considered Funakoshi an ineffectual charlatan.

Above: In this 1936 meeting Okinawan masters including Chotoku Kyan, Kentsu Yabu, Hanashiro Chomo and Chojun Miyagi, discussed the change of terminology from "Karate Jutsu" to "Karatedo" and from "Baida" (Hakuda) to "Judo" (sic. Jujutsu)