I've been thinking about how to articulate a thought I had about a possible Doylist/non-diegetic reading(EDIT: I originally wrote "Watsonian" here, which is the opposite of what I meant X| X| Brain, you Tricksome Jester *shakes entirely metaphorical fist*) of Eridan's Trollian handle, caligulasAquarium, in response to a post of @mmmmalo's, and I think I've got it.
Ok So: the popular perception of Caligula is as a "Mad Emperor". One of the points used in this depiction is his "War on the Sea", which is taken as obvsl absurd and empty and irrational(and possibly hubristic). Eridan chooses to call himself "caligulasAquarium" and he lives in a wrecked ship(a feature commonly put in aquariums)... on the surface.
So like: maybe the title is meant to be taken by the audience as ironic. Eridan's claim to an "Aquarium" is as absurd and empty and irrational as Caligula's claim to have warred upon the sea(in the common understanding of those events; as a matter of history this seems to be a Telephone distortion, from the sources I can find).
A few more points that have occurred to me since I started writing this:
Caligula "Made War on the Sea"; Eridan wants to "Make War on the Surface" by Killing All Landwellers, carrying forward the themes of inversion btwn Alternia and Earth.
Also: "Kill All Landwellers", "Kill All Humans": he's lampshading common evil-alien-overlord tropes
...Which in itself is sort of dunking on HIM, since Eridan is nobody's overlord he's just some GUY. Like: Yes, he's "Nobility" due to blood-caste, but he has no influence, no power, no RESPECT from anyone we meet, no friendships let alone alliances with other socially powerful individuals(other than Feferi, who seems to have foresworn all that to monastically care for G'lybgolyb) that he could USE to have influence; he's just a loner with his grand-dad's gun and allot of pretension.
...which you could argue furthers his parody of USian internet white-supremacists? Like: He is THEM: a gun-humping loner who only feels comfortable talking to the people he claims to hate, with no idea how unpleasant he makes himself to interact with, and even less interest in introspection or self-awareness, fetishizing past genocides as a way to claim for himself a "Glorious Past" he had nothing to do with.
As Feferi(and possibly other characters I'm forgetting) point out, Eridan's ambition to Kill All Landwellers is more than a little absurd. He's never really DONE anything to plan or prepare for it, and aside from Fef he exclusively hangs out with and befriends Landwellers, as well as LIVING ON LAND(well: a sandbar or reef). This could be taken as furthering the Caligula "War on the Sea" parallel.
Expanding on the last: Caligula, THE EMPEROR OF ROME and Grandest of Nepo-babies, was rather notably disdainful of and hostile towards the Roman nobility and inherited wealth/rank. This connects to Eridan in two ways I can think of: 1) his avoidance of other seadwellers, and 2) his philosophical hostility to landdwellers while Being, in practice, A Landweller. Basically: both Hate things about themselves shared by others.
Reinforcing #3: the choice of Caligula, a Troll-Emperor. Again: Eridan is Just Some Guy; he does not command armies, he does not command society, he can't even command Equius, who GETS OFF ON being ordered around. This is Pretension.
...which, I guess, you could connect AGAIN back to Caligula via the popular memory of him wanting to be treated "As A God", but it should be noted that 1)everyone who wrote anything about him hated the guy and was explicitly dunking on him, so we don't know how accurate these charges are, and 2)in the Roman context, while legal apotheosis was reserved for after death, imperial Divinity was already de facto given that sacrifices and prayers to the Emperor's health and success were legally mandated civic religious duties, AND 3)that classical Greeks and Romans, contra the Abrahimic societies which would later create this popular memory, considered apotheosis a real possibility for notable individuals.