The Wrath Confessions are confessions of sins related to the theme of Wrath, that the Demon King worshippers confess to the demons to hear their words and Satan's veredict.
Confession: You're called "Lady Leviathan" [read: Reviatan], but if it's like the sea monster feared in various areas, shouldn't you be "Leviathan"? [read: Rivaiasan]
Eh! Then, Levi has become greater?
Yep, yep, it's something like the fishes whose name change when they grow up. Congratulations... Ah! Yahoo, Asmo-chin, he-llo. Listen, Levi-chin has leveled up.
Oh my, congratulations. You'll be "Levia-san" from now on.
Ooh, what, what, is that true? "Levia-san", isn't it nice?
Looks like you'll be like Sazae-san somehow. This way, without a youth...?
"Levia-tan" is fine. I don't need a promotion.
Satan: Sin of Wrath, level 2. Following "-tan" and "-san", will it be "-sama"?
-Note: besides the usual romanization of "the" Leviathan, there's also a pun going on here about how she's usually nicknamed "Levia-tan" and now she'd be "Levia-san", like Satan points out later. Also, I'm not really sure if Lucifer's referencing that manga, but she's probably referring to Leviathan being more mature now, which Leviathan doesn't really appreciate.