I wonder where this whale Twain got its name? assuming the whale-namers named a bunch of whales (at once or over time) it's really appropriate that this particular whale participated in this particular landmark conversation.
One of the most popular, distinctly-American authors of all time, humorist Samuel Clemens, wrote under the pen-name "Mark Twain". He was very skilled in his use of language for communicating his musings, and the "sound" of Twain's phraseology is quite pleasing.
his pen-name comes from the phrase "mark twain" which was shouted by sailors on riverboats as part of their measuring the depth of the water, mark twain (2) referred to 2 fathoms (12 feet, 4 meters-ish but it was measured with a weighted stretch of rope, so is "twine" a stretch?)
Measuring the depth of water is alternatively called "sounding", and not even because of sonar, but because nautically speaking a sound is also the name for a small but deep enough to be navigable body of water. Whales dive into the depths of water, and that is also called the whale sounding.
But of course, this communication is using the audible sounds of whale vocalization. A connection between two parties communicating could be called "where the twain (2) shall meet". or if it's groundbreakingly successful moving forward, e'er the twain shall meet. (compare "ne'er the twain shall meet")
I can't imagine all these literary allusions were part of the naming decision, unless she/he was named as part of the experiment, so I think it's just a fun sequence of collisions.