Why "By the Power of Eternia"?
Adam says "By the Power of Grayskull" in the first episode of The New Adventures of He-Man. But by the second episode, the phrase is inexplicably dropped and replaced with "By the Power of Eternia".

The toy line's explanation is revealed in a mini comic, where the Power of Grayskull is channeled into Starship Eternia. But by that point in the comic, He-Man sheds his Adam persona. Obviously the mini comic continuity is NOT in sync with the cartoon...

There is thus no definitive answer for the cartoon series, as the Starship Eternia does not serve the same purpose as in the mini comic.

Here are my theories:

1) It's possible that in this future, Castle Grayskull no longer exists, and so the Power comes from the planet Eternia itself.

2) With the big focus in the previous toyline shifting to the Eternia playset (in the mini comics, I believe the playset was more powerful than Castle Grayskull - since in the mini comic "The Ultimate Battleground", the Eternia playset becomes more important than Grayskull), perhaps "By the Power of Eternia" refers to it.

3) This is a retroactive idea: Maybe "By the Power of Eternia" is the original summoning cry that was used before and during King Grayskull's claiming of the sword of He (this idea ties into the concept of the Power being a force created by, or existing within, the planet Eternia itself).