Hi. I hope I have understood you question.
The rule is valid only for masculine names (Signore, Dottore and Professore)
You can use Signor, Dottor and Professor only referring to a man.
Il Signor Bianchi (it means that Bianchi is a man not a woman)
If you say "Il Signore", you referring to a man
La Signora Bianchi (Bianchi is a woman)
La Signore (without a name)
If it's not clear or if you have question, let me know....If I can, I'll help you! Bye for now