If you believe that giving your black mirror a name will increase its power, then go ahead and give it one. I named my 1st computer, Arachne, spinner of webs and together, we created award-winning websites. Neil Finn named his keyboard Paul, which I believe to be a tribute to his dear departed bandmate.
As for naming genitals, that’s an interesting one. My ex would refer to “Willy” and we’d refer to “him”, as though “he” were a little person. I liked this. I have always had a rapacious sexual appetite and many of the guys I’ve been with refer to their member as “him” or “he”, whether or not they give it an actual name. One guy referred to my vagina as “she”, which creeped me out, for some reason. I don’t know why, given I was perfectly comfortable with the personification of male genitalia, having heard it so many times. This guy was creepy, to be sure. He was a talented songwriter and went on to tell me about the number of poems he’d written about vaginas. “It’s the gateway to a woman!”, he declared in his coked-up state. I openly scoffed at such a statement and shortly excused myself from this creep’s presence. Have another line, cos you ain’t getting none of mine! I digress.
I would be interested, Black Flame in the name you come up with and the significance thereof. Yes, a song needs a name for reference, but sometimes choosing one can be very hard indeed. Everyone knows “Bohemian Rhapsody”, but how did Freddie Mercury decide on such a name -and how, indeed did Blur come up with so creative a title as “Song 2”?