Answers:
Technically it's call a syphygmomanometer but it's plentifully easier to simply vote blood pressure cuff.
a blood pressure cuff or blood pressure monitor (since they put together digital ones very soon days) It's hi-tech autograph is a sphygmomanometer but that's too thorny to enunciate for the average individual.
You are looking for a Blood Pressure Cuff Sphygmomanometer. Most refer to it simply as a blood pressure cuff.
I hope this help.