As any woman of any era immediately recognizes (Mr. Moffat and Mr. Gatiss really need to acquire some females on their writing team, not just their production team), "The Woman" is not, despite Watson's protestations, a compliment, but an insult. It implies that the most important characteristic of Miss Adler was her gender, not her intelligence, talent, kindness, or any of the other attributes with which Conan Doyle endowed her. As I shall discuss at greater length elsewhere, Holmes despised Miss Adler by the time she ran off with her new husband, and his epithet for her is an abbreviation of "The Woman Who Had the Unmitigated Gall to Be Intelligent Enough to Beat Me!"
Therefore, it should have been left in the nineteenth century, where such chauvinism belongs. It's long past time that men got over the reality that women can and do think and stop pretending that there is something exceptional in a woman's doing the most trivial of mental exercises. Miss Adler "eclipses her whole sex" (emphasis mine) by coming to two very obvious conclusions (one, that she'd been tricked into showing her hiding place; two, that her best alternative was to flee London)? As much as I admire Miss Adler (as I will go into detail in a later article), it hardly qualifies as brilliance on her part, and that Holmes thinks it does shows how low his estimate of women is in general. That Mr. Moffat did not understand he was insulting his entire female audience by taking Holmes's prejudice seriously and using Holmes's insult in his episode is no less abominable for being very typically male even in the twenty-first century.
Even if it had been a compliment, Miss Adler never used it to refer to herselfindeed, she never heard it!and it is too generic to make a good trade name (see items 3 and 4), as any self-employed modern businessperson would recognize. It would be like my trying to brand myself with "The Editor"; how are my customers ever supposed to find me in the sea of editors out there? I suppose it is what one should expect of people who named their series simply "Sherlock" in a culture full to the brim of Sherlock Holmes references, but they could have asked someone in their advertising department what they thought, although those people might not be speaking to them for naming their series so generically!
"The Woman" is so very insulting and worthless in the context given that even its origin in the Sherlock Holmes canon cannot make tolerable its continual repetition in "A Scandal in Belgravia."