Does BPM change during a song?
In most songs (especially popular music), the basic tempo doesn't change throughout the song. However, there are musical concepts that involve speeding up or slowing down the tempo. One of these we've already seen: rubato, or slight expressive changes in tempo.
What is it called when a song changes tempo?
It's called a tempo change, unless the tempo stays the same but the key changes in which case it's called a key change :P. Though if you want all the technical sheet music terms : http://en.wikipedia.org/wiki/Tempo#Terms_for_change_in_tempo.