In his autobiography "Eye of the Hurricane", Richard Bellman explains the origin of the name:
“I spent the Fall quarter (of 1950) at RAND. My first task
was to find a name for multistage decision processes.
“An interesting question is, ‘Where did the name,
dynamic programming, come from?’ The 1950s were not
good years for mathematical research. We had a very interesting
gentleman in Washington named Wilson. He was
Secretary of Defense, and he actually had a pathological
fear and hatred of the word, research. I’m not using the
term lightly; I’m using it precisely. His face would suffuse,
he would turn red, and he would get violent if people used
the term, research, in his presence. You can imagine how he
felt, then, about the term, mathematical. The RAND Corporation
was employed by the Air Force, and the Air Force
had Wilson as its boss, essentially. Hence, I felt I had to do
something to shield Wilson and the Air Force from the fact
that I was really doing mathematics inside the RAND Corporation.
What title, what name, could I choose? In the first
place I was interested in planning, in decision making, in
thinking. But planning, is not a good word for various reasons.
I decided therefore to use the word, ‘programming.’
I wanted to get across the idea that this was dynamic, this
was multistage, this was time-varying—I thought, let’s kill
two birds with one stone. Let’s take a word that has an
absolutely precise meaning, namely dynamic, in the classical
physical sense. It also has a very interesting property
as an adjective, and that is it’s impossible to use the word,
dynamic, in a pejorative sense. Try thinking of some combination
that will possibly give it a pejorative meaning.
It’s impossible. Thus, I thought dynamic programming was
a good name. It was something not even a Congressman
could object to. So I used it as an umbrella for my activities”