1stLady,
I'll try to answer your question.
As far as the name of the chord, I believe it depends on the scale you are using. For example, if you are playing in the key of "G" major, then it will be called "F#M7"... but in the key of "Db" major, it will be called "GbM7".
Now, in terms of the sound...
If you are using the "F#" or "Gb" in the left hand bass, then the tonality of the chord isn't changing, and the context of how you are using the chord in a progression determines what purpose it truly serves.
"GbM7(b5)" is: Gb Bb C F in the key of "Db" major, root position.
I'm sure, someone else will expand what I am saying, but I hope this helps.
God bless,
Eggs