The full name of the sword style practiced is Muso Jikiden Eishin Ryu. For better understanding, we need a small introduction into the history of Japanese swordsmanship.
In old feudal Japan (14th to 16th century) existed already a great number of different sword schools, each competing one another. A certain Hayashazaki Jinsuke Minamoto no Shigenobu, who lived at the end of the 16th century, was the first one to formalize a number of techniques and called his system Batto-jitsu. He is considered as the father of all modern Iai-do schools.
Successive grandmasters changed and putted the system further to perfection. The 7th grandmaster Hasegawa Chinaranosuke Eishin, added a remarkable improvement: the cutting edge of the sword was turned upward so unsheathing became more practical.
The name of the school changed later from Batto-jitsu into Muso Jikiden Eishin Ryu, in memory of the 7th grandmaster and to honor his improvements. The meaning of the name is: the by the Gods inspired and direct transmitted style of Eishin.
Eishin Ryu is a style that traces back, in a continuously uninterrupted lineage, to Hayashazaki Jinsuke Minamoto no Shigenobu.
A lot of people practice Eishin Ryu; even outside Japan, but most of them never had contact with the Soke or with one of his direct students. This resulted in a lot of differences for the same style.