There's no such thing as authority to name a whale, and anyways I don't believe authority is strictly needed. A name is what people use to refer to something, full stop. It is only required that names become common-ish parlance; the more well known they are, the more they feel like the 'real' name. The inverse of Ohms is named Mhos (imo much more recognizable than the official name, "siemens"). The "#" symbol is named the hashtag, octothorp, pound sign, tic-tac-toe, number sign, and probably a million other things. Which one of these is the "real" primary name? I think intuitively we know that the real one is whatever people around us are most familiar with. You should take a guess, and I'll put the wikipedia-suggested-answer in the footnotes [1]. I bet your name for it is different than the 'official' wikipedia suggestion.
In the case of the whale, the _only_ name that is associated with that whale is Teresa T. I think this immediately makes it the most valid name of that whale.
[1] wikipedia says this is the number sign: https://en.wikipedia.org/wiki/Number_sign