What's the significance of the witches' name change in Sandman?

Question

As mentioned in another question, the three witches are very significant in The Sandman. While that other question asks for their significance in general, I have a much more specific question to ask.

In issue #2 ("Imperfect Hosts"), Dream returns to his home after escaping captivity on Earth. Finding things greatly changed from how he left them, he realizes that he must recover his tools and fix things. He summons the Hecateae, and calls one of them by name. This kicks off a discussion about how the witches prefer to be called.

Dream: "Lady Atropos, you have found me out. I DO want something."

Crone: "Atropos? No. Not now. You might as well call me the Morrigan!"

Allmother: "She's right, my ducks. Might as well call us Tisiphone, Alecto, and Magaera -- and that takes us back, eh?"

Maiden: "Might as well call us Diana, Mary, Florence and Candy. Ha ha! Uh, sorry."

Dream: "For me, you will always be the three graces, ladies."

Voice off-panel 1: "Flatterer!"

Voice off-panel 2: "Ooh, he's the clever one!"

Dream: "So what should I call you?"

Maiden: "I'm Cynthia."

Crone: "She's Mildred. I'm Mordred. Stupid name. I ought to be Morgaine."

Allmother: "It wasn't my fault. I just got them confused, was all!"

^{The Sandman #2 "Imperfect Hosts," page 19}

(Note: another version of this panel, provided by Gallifreyan, records only three names, leaving out Candy)

When Dream finally asks them for help, he addresses them by other names:

Dream (to the young witch): "MAIDEN, there was a POUCH of SAND. It was stolen from me."

Dream (to the kindly older witch): "I SEE. Then your question, ALL MOTHER. My HELM -- what happened to it?"

Dream (to the oldest witch): "CRONE. A final question, for you. My STONE, my DREAMSTONE, my RUBY MOONSTONE. Who has THAT now?"

^{The Sandman #2 "Imperfect Hosts," page 21}

So I have, essentially, two questions about this exchange.

1. What is the significance of the name change?

As I understood it, Dream called them by names that he was likely using for millennia. Did they change names because of the general weirdness that happened during Dream's 70 year absence? I infer from the Crone's statement ("Atropos? No. Not now.") that the names were changed from what they were before ("not now" as in "not anymore").

Does this name change have a deeper meaning?

2. What do the different names represent?

I am not very well versed in mythology; these names don't mean much to me. I was able to find some things during my preliminary research for this question:

• I found that Alecto, Megaera, and Tisiphone are the names of the Erinyes. (Found that by searching Wikipedia for "three witches comics," and finding a mention of the Erinyes on a page about a volume of The Sandman that I haven't yet read)
• I found that the Morrigan is a figure from Irish mythology, a "phantom queen" who represents fate.
• The most relevant result that I found by searching the web for the "Diana, Mary, Florence and Candy" was this page, which is very light on the background for these names. I'm also confused about how the Maiden gave four names for three persons.

In summary: Why did the three change their names now, and what do those different names mean?

Answer 1

The Three Witches appear multiple times in the Sandman series, often showing a penchant for trickery and subtle jokes. Here, they are giving Dream a hard time about their names, comparing several Triple Goddesses and throwing in some pop culture references for fun. This implies that they consider themselves to embody aspects of the Triple Goddess, across many cultures.

1. Clotho, Lachesis, Atropos: The Fates, Greek mythology
2. The Morrigan: three sisters of war, Irish mythology
3. Tisiphone, Alecto, Megaera: The Furies, Greek mythology
4. Diana, Mary, Florence: The Supremes, R&B trio (Florence was replaced by Candy/Cindy in a later lineup)
5. The Three Graces: aka The Charities, Greek & Roman mythology
6. Cynthia, Mildred, Mordred: hostesses of The Witching Hour comic by DC (Mordred should have been Morgaine in Arthurian legend)
7. Cynthia is also an alternate name for Artemis, of the Selene-Artemis-Hecate trio
8. Maiden, Mother, Crone: many versions of the Triple Goddess carry these titles, allowing Dream to dodge the thorny issue of which names to use

References:

• The Annotated Sandman. Edited and largely written by Greg Morrow.
• The Sandman: Preludes & Nocturnes (unresponsive link, verified on 26.12.2020).
• Three Witches, in DC Database.
• Triple deity (Wikipedia).