The origin of Impa's name was revealed in the new Zelda history book, Hyrule Historia.

Miyamoto explained that Impa's name comes from the word impart, due to the fact that she imparts the legend of Zelda.

In the same section of the preface, Miyamoto re-explained the origins of both Zelda and Link's names. When creating the character Zelda, Miyamoto knew he wanted it to be "Legend of" something. He also knew he wanted the character to be a timeless beauty. Zelda was suggested because a famous writer's wife, known for her beauty, had this name (Zelda Fitzgerald). Miyamoto liked it, so he continued to use it. 

Link is supposed to be a character that links the energy throughout the world and transcends time, hence the character was named Link.