Any name in Japanese ending with the kanji "-kan" actually refers to an organisation, association or specific dojo. A rough translation would be "house" or "club". Thus "Bujinkan" means something like "martial spirit house" and Genbukan "virtuous martial house". I'm not sure about Jinenkan, as I'm not aware of what kanji they use to write their name.
The names they use for what they teach, however, don't translate so easily. Roughly, "budo taijutsu" means "martial-way body skill" and "ninpo bugei", "endurance-method martial technique".
It seems to me that the schools are now using these names because "ninjutsu" (a) only covers part of what they do, and (b) hasn't been cool since the 80s. When Hatsumi first became popular outside Japan, calling his art Togakure Ryu ninjutsu (which actually only forms a small part of the Bujinkan syllabus) attracted the punters because everybody had seen a Sho Kosugi movie and wanted to learn to do all that. Now ninjutsu doesn't sell, they can afford to be more honest about what they do, calling their style by a name that more accurately reflects what they teach.
__________________ Hengest
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