Back in the `70's the combative sword arts we  practiced was simply known as "Shinto Ryu Kenjutsu".  The name had been lost to history but was roughly analgous to the name "Smith".  It was a very common catch all name. Shimizu Sensei himself when asked about the art's name and origins could not provide much additional detail. 

Research in the '90's spearheaded by Mr. Kaminoda and supposedly  authenticated by the Imperial Household's Historical Archives Division revealed that the original name  might very well have been "Kasumi Shinto Ryu" although most Jodo exponents today still refer to our kenjutsu as Shinto Ryu. The densho or scrolls handed down from generation to generation and recently found in family archives lists 12 kata that reflect the same 12 kata previously known thru oral tradition as Shinto Ryu.

The study of the ken (sword) within Jodo was historically learned only after achieving some mastery with the stick. Appearing deceptively simple the ken  or sword as practiced with a bokuto (wooden sword for contact training) is quite challenging to learn and master. Today some teachers are rushing to teach the ken to students not yet well versed in Jo.  While in small groups this might not be completely avoided it should be minimized by anyone seriously trying to learn Jodo.  The fact is that unless Uchidachi (sword partner) understands the movements, the kata will not become alive and the Shidachi (stick partner) will not gain proper understanding.  The damage done however is that there is an illusion of sorts because the kata is performed albeit without proper heart.   It is interesting to compare movements when looking at how the ken is used for both tanjo and jutte as well.  Arguably I guess, this style of Kenjutsu is one of the oldest to survive history and still be practiced.