Probably it is worth mentioning 我儘の極意, considered as a combination of ordinary words, makes little sense. As such anything may be fine as a translation as long as it vaguely reminds of the original, so I guess Ultra Ego is good enough.
The naming seems to be a kind of wordplay.
Apparently, Goku's new transformation uses a word 身勝手, which means selfishness. But the author takes it as 身(body) + 勝手 (as in 勝手に=instinctively, automatically), so the intended meaning is like body moves instinctively.
Now 我儘 also means selfishness, and that seems to be the reason of the word choice. Again, the author's intention is breaking it down as 我(I) + 儘(as) = as I wish/want. (This may be not too far from the original meaning anyway.)
極意 means something like ultimate technique. For example, to get 極意 of X in Japanese means a complete mastery of X.
Thus a bit awkward translation of 我儘の極意 is the ultimate art of moving as I wish.