The first one was always intended to be called
First Blood
after the novel it was based upon. It was in non-English speaking foreign markets, where the idiom "first blood" has no real meaning, that it was changed to
Rambo
.
The sequel was originally to be called
First Blood II: The Mission
, but changed by Stallone to reflect the foreign market, where the first film had done much, much better. The 3rd was actually titled
Rambo: First Blood Part III
in some foreign countries.
Even the fourth film had a fake working title (according to imdb trivia) of
Rambo: First Blood Part IV
.
What do you say, you dumb bitch?

See trivia for Rambo 2. Stallone wanted to change the name but kept the First Blood part so people knew it was a sequel. Sort of like John Cougar Melloncamp.