The "Rough Guide to the History of England" describes the two of them as having been jointly called "the Elephant and Castle", but on the Internet I find another story.
calls the thin one the "Maypole" and the fat one the "Elephant and Castle". Might be at least one instance in which the Internet source is more reliable than printed paper.
has a long article on the Hannoverian succession. The author claims that the story about Baroness Sophia Charlotte von Kielmannsegge (afterwards Countess of Darlington) having been George's mistress is incorrect and can be traced back to the malicious pen of the Margravine Wilhelmina of Bayreuth. The King is said to have acknowledged and honoured his half-sister as being his half-sister, and not a mistress.
Anyway the affairs of George I may have been less exciting than it seems as
[From waterford-online.ie 2005 article, no longer online]
claims (OTD-11 June 1727) that the King spent most of his evenings with Ehrengard Melusina von Schulenberg, "indulging their shared passion for ...cutting out paper pictures."
"The Maypole" or "Scarecrow" is said to have had "the proportions of a rather aged lamp-post and about as much personality". Hard to recognize a "Castle" in her.