What is the name of the weapons training used in ishn ryu?
Isshinryu (or Isshin Ryu), the Okinawan karate system founded by Shimabuku Tatsuo Soke, has an integrated kobudo or weapons system. It does not have a name, per se.
As most karateka know, the word 'karate' by itself means 'empty hand' (it once meant 'China hand'). Therefore, technically no karate system would have a kobudo component to it. But Isshin Ryu has one.
It consists of the bo, sai, and tuifa (tonfa). There are several kata for each, except for tuifa, for which there is only one kata.
Now, having said that, one of Shimabuku Soke's students, Tokumora Kensho Sensei, has developed his own style of kobudo, known as Tokushinryu Kobudo.
Tokushinryu Kobudo -
This is an extensive system that uses a larger number of Okinawan weapons, and kata which were created by Tokumora Sensei himself (for the most part).
I am currently studying it, although I am not yet a member of the organization and I hold no rank in that system. Our dojo has affiliated with Tokushinryu Kobudo and we will eventually be gaining rank in that system, I presume.
Since Tokumura Sensei was a first-generation student of Shimabuku Soke and is a very good friend of Isshin Ryu karateka around the world, it's not uncommon to see the two systems side-by-side. However, not all Isshin Ryu karateka study a separate kobudo system, and of those that do, not all of them study Tokushinryu Kobudo.
I hope that answers your question.