He discovers that it not only appears like a small apartment furnished with a well-loved ratty armchair and a goldfish bowl, but is cluttered with fishnet stockings and jeans draped casually over the furniture. When Death arrives, she tells Orpheus that it's just that way because that's how she prefers it, and then changes it into an ornate hall of mirrors for his benefit. Destiny, the most serious of the Endless, often chastizes Death for wearing inappropriate clothing to family gatherings. Death's faded black jeans and tank tops don't sit well with Destiny, and he urges her to change into Victorian era mourning clothes. Linear continuity is not a primary concern of Gaiman's and would not work in accord with the fluid, shifting narrative that often reads like a dream, where things change for no particular reason.
Dreams have their own grammar and own set of meanings.
This changing is simply accepted and does not seem ridiculous in the context of the dream. For example, Delirium's appearance is consistent only in inconsistency. Her wildly colored hair appears long in one panel, short and one shade in the next, and a few panels later her hair has begun to grow back but in a different color. Her clothes are constantly changing, from a torn fishnet bodysuit in one panel to a cocktail dress in the next. These changes are obviously meant to reflect her unstable mental state, but do not keep the reader chronologically oriented.