Kenpo or yawara (拳法)

Presently, kenpo and yawara mean martial arts with bare hands using striking and kicking techniques.. It seems that the so-called 'kenpo,' which has spread in today's world, mostly originated in Asia, though there are various theories. Among Japanese jujutsu there are schools naming themselves kenpo, but it is Chinese name of jujutsu which is often read 'yawara' while it is written kenpo (拳法). It is not so that those schools have more striking and kicking techniques.
(there is no relationship between the name and the number of striking and kicking techniques.)

Summary
It is not a historical fact, but according to a legend, the origin of Shaolin kung fu is the mental and physical training method that Dharma brought from India and taught in the Songshan Shaolin Monastery.

Chinese martial arts (kenjutsu) are roughly divided into two groups according to geography: southern (ex. wing chun quan, hung ga kuen) and northern (taiqiquan, bajiquan, etc.)
The northern group is sometimes divided into the internal and external groups. There is a theory that the external group, including Shaolin Kung Fu, features the integrity and strong way of fighting, and the internal group, including Taiqiquan, features the seemingly-sluggish movement holding power inside the body along with breathing, but they were classified in recent years and in fact both groups have a combination of those features.

In Japan, it is said that Chen Yuan-Yun from Ming brought it in the late 17th century and his disciples modified it to suit to the Japanese climate as a kind of Jujutsu. But in fact, many forms of Jujutsu, martial arts with bare hands, had existed before he came to Japan. Also the schools purporting to be taught by Chen Yuan-Yun to gain prestige don't necessarily have techniques like Chinese martial arts. There is actually no record that Chen Yuan-Yun himself practiced martial arts.

Chinese martial arts also affected the establishment of karate.

Kenpo in Japan
Presently in Japan, shorinji kenpo and nihon kenpo are famous - the former has spread among a wide range of people within background of a new religion and the latter has spread among some groups centered on university kenpo teams and turned into a sport in a sense – but both are performing activities such as showing their techniques on TV. Both are martial arts and combative sports that have been developed based on Japanese martial arts.

Shorinji kenpo, which was started by Michiomi (the future Doshin) SO and has developed based in Kagawa Prefecture, and Nihon Kenpo, which was started by Nuneomi SAWAYAMA (born Masaru SAWAYAMA) and has developed centered in Osaka Prefecture, are totally different Kenpo.

Shorinji kenpo

Shorinji kenpo is a Japanese martial art developed and established by SO based on various Chinese martial arts which he learned when he stayed in China to work for the secret military agency before and during the war, adding Japanese Jujutsu, which he had learned when he was a child. It has a system of techniques centered on the art of self-defense and philosophies such as 'self-definition,' 'mutual comfort,' and 'not competing in strength,' which have been accepted by a wide range of people, and it has spread in 31 overseas bases having 140 thousand members worldwide. It is often confused with shaolin kung fu of the Songshan Shaolin Monastery, but it has a totally different system of techniques.

Nihon kenpo

SAWAYAMA, who was a Judo expert at that time, found that striking and kicking techniques included in the judo forms were not practiced; therefore, to establish the training system he originated dainihon kenpo based on karatedo and others and renamed it nihon kenpo after the war. It features making attacks in which the participants put on the original protective gear, and the system of techniques was developed by mutual influence with karatedo and others. It has produced world champions such as boxer Jiro WATANABE and kickboxer Genshu IGARI (the current chief grand master of a non profit organization called Nippon Kenpo Kyokai) and it is known that the techniques have been adopted as the model for Japan Self Defense Force MMA and arresting art of the police. It is notable that it was quick to establish the form of jiyu kumite (free sparring) (presently the word 'kumite' is not used in nihon kenpo).

While the situation is as stated above, there are also some jujutsu schools in Japan that have many striking and kicking techniques.
There are existing representative schools such as Yagyu Shingan Ryu, Shosho Ryu, Tenjin Myoshin Ryu etc., but they don't call specially themselves kenpo
There are are also schools established in modern times that call themselves kenpo such as Wadoryu Jujutsu Kenpo, Shinto Tenshin Ryu, etc.