According to the Oxford English Dictionary, the exercise was named in the 1930s for American psychologist Royal H. Burpee, who developed the Burpee test. Consisting of a series of the exercises performed in rapid succession, the test was meant to measure agility and coordination. It is not clear whether the exercise itself was invented by Burpee, or if his test merely popularized it. (Source: wikipedia.org)
I remember the first time I heard "burpee." I was taking a group fitness class in London, England and the instructor demonstrated a burpee. I then realized it was a squat thrust. Perhaps there is an English connection?