So now that we have the original trio's names, lets dive into them and what they mean.
Leif is a Scandinavian name, who's meaning of old is "Descendant" or "Heir", which seems to not refer to her, but rather the family who inherited her hunting dance.
Also, though it has nothing to do with it, English speakers usually butcher this name as "Leaf"(As happened in the show), when it would actually be pronounced similar to the english word "Life".
Either way, both those fit Leif quite well.
More interesting is that it is also the name of Leif Erikson, the legendary explorer who was the first European who ever set foot on American soil. And unlike Columbus, he did so without committing genocide on the locals, which mirrors Leifs arrival to Earth, which ended up saving the planet from Amphibia's warmachine.
As the only one of the trio with two names, Andrias Leviathan has two very different origins.
Andrias is the name of a certain kind of real life enormous Salamanders, which presumably is the Earth counterpart to his species.
Andrias is also an old scandinavian corruption of the name Andreas.
Andreas is an ancient greek name which means both "Man, warrior". As in, the name referred to the duty of a man in Ancient greek, first and foremost of which was to protect his home and family, hence the name becoming associated both with familial(Of the male variety) duty, and being a warrior, mixed into one.
Both of which fits Andrias very well, being the only son and heir of a king, and expected to continue it's imperial conquests as his duties, while also being a formidable warrior in his own right.
Meanwhile, Leviathan is an ancient, biblical, beast, the embodiment of the sheer power and chaos of the seas.
Fitting for a man who brought nothing but destruction and pain to his people, and wishes to do the same to every other world.
Also, Andrias is seemingly one of the last Salamanders in the world, which fits in well with the fact that according to Jewish tales, there was originally one male, and one female Leviathan, but after creating them, God realised that that if he let them multiply, they would go on to dominate all life in the sea, and so he killed the female one, leaving only the male Leviathan left, to forever swim the oceans alone and lonely.
A barrel is the container used to store things, and many of them have the same build and shape as the midsection of Amphibian's toads. Round, strong and Stocky.
As a word, it has several older meanings, such as "Of uncertain origin", "Bolt", "Bar", "Jug".
However, that is not to say that there isn't a deeper meaning to his connection to his namesake.
Though today we tend to think of Barrels as common things, in the old days, Barrels were very valuable and valued things, that required very skilled laborers to make, in order for them to be a sealed vessel for liquid.
In particularily, they were buried with the dead as grave goods.
And as it happens, Barrel's main contribution to modern Amphibian history, is his own grave good, his hammer, that marks where he died.
The of course there is the fact that Barrel(Which were necessary to store achohol such as beer) was known as "Barrel the Brave", and as anyone who has any knowledge of soldiers can tell you, there is a reason why "Liquid Courage" is a term.