In schools, students were usually addressed by their last name by teachers. This custom was adopted by boys and persisted into manhood as an address for friends and acquaintances. This is why Holmes and Watson nearly always call each other 'Holmes' and 'Watson', not 'Sherlock' and 'John'. (In fact, the only time in the stories when one used the other's first name was in "The Adventure of the Three Garridebs", when Holmes was trying to bring Watson out of unconsciousness.)
Women were usually addressed as, say, "Miss Lestrade" if she was the oldest daughter, and "Miss Elizabeth" if she was not. (Men were often similarly addressed; if Mycroft Holmes was the eldest Holmes brother, no doubt the folks in Sussex would call him "Mr. Holmes"; if not, he would be "Mr. Mycroft".) Some women adopted the male habit and addressed their close female friends by their last names, but this was unusual; women were more likely to use their female friends' first names.
So when Holmes calls Lestrade by her last name, it means that he regards Lestrade as a friend or fellow professional, just the same as if she were a man -- an interesting position for a Victorian to take, even for one who lived through the flapper era. (Moriarty's initial use of "Miss Lestrade" was probably intended to be polite, although Lestrade found it insulting since it ignored her hard-won title of Inspector.) It is highly unlikely that Holmes will ever call Lestrade "Elizabeth" or "Beth" on screen -- and if he does, he will be declaring that he regards her as a very intimate friend indeed! UPDATE: He did refer to her as Beth, to Watson, in TWIS2!
On the other hand, Holmes' use of Deidre's first name signals that he regards her as a child. (Which incidentally absolves him of worrying about the proprieties, even though she is a fairly mature-looking 12-year-old. If indeed, the poster is to be trusted on her age.)
One more point of interest --
Holmes uses the friendly endearment "My dear X" to Watson and all of the Irregulars. But though he referred to her (to Watson) as "our dear Inspector Lestrade" in DERA, and included Lestrade in the group he called "My dears" in RESI2 as well as calling her "dear Lestrade", he has never used the words "My dear Lestrade".
No doubt Holmes wishes to avoid encouraging people like me or the Watson of old. Well, then, he shouldn't be calling the woman Beth!
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