The Stage Shows Duality
The stage appears as a metaphor for the dichotomy between real and perceived life -- Margo first appears brilliant onstage, then tired and jaded offstage. Similarly, Eve seems unassuming in her first few scenes, which is why Margo takes her in, but once she makes it onstage, she shines, showing her true ambitions.
Age and Relevance
Age is a frequent stand-in to refer to Margo's relevance as an actress. When the issue of casting her of Cora comes up, she rebukes the idea that she would play a "twenty-ish" character, insisting that she is forty years old and she is a talented enough actress to remain relevant despite this. On the other hand, when Eve appears, her youth is primarily what makes people interested in her as an actress.
Rain as Insignificance
Rain appears as a metaphor for insignificance in the film -- Eve first appears in the rain as a bedraggled young fan, and later refers to the place she is from as "a drop of rain in the desert." Rain covers those who are fading out of significance are frequently covered in rain.
Furs Signify Success
When Eve goes to a party, she sees a pile of expensive furs on the bed and learns that they belong to the Hollywood elite at the party. Margo frequently wears fur as well. For these elite actors, wearing fur signifies success and fame. When Karen says "Women with furs like that where it never gets cold," she's referring to the excess that comes with Hollywood fame and wealth.
Names Have Power
Names are a metaphor for status. Eve changes her name in order to appear more respectable and glamorous. Similarly, the names of famous actresses and theater critics are used as tools -- invoking them causes a reaction. Meanwhile, low level people's names are never known -- when a party guest wants to call for a butler, she says "I can't yell "Oh, butler," can I? Maybe somebody's name is Butler," implying that calling out for staff in that way might offend a person with that name.
