The answer is yes it is still a G7 chord. When the root of the chord is not the bass note the chord could be written with the bass note after a forward slash. For your G7 example it could be written G7/F.
This would be call an inversion. G7 normally would be written G-B-D-F. A first inversion would be written B-D-F-G, a second inversion is D-F-G-B, etc. The first and second inversion could be written G7/B and G7/D.
The bottom line is the notes in a chord determine the chord name, not the bass note.
Thx, Mario. I've always wondered what those notations meant. Now I know.
I notice you play the flat 7 in order, after the 5.
This may be a quirky comment, but I'll make it anyway: I was lucky to have been pointed in the right direction. First, I learnd to read melody staffs. Getting serious about pop (country) years later I committed the twelve major 135 chords to memory. Using home made backing tracks on a multi track portable cassette recorder, committed those twelve keys to absolute memory by playing along with those 12 backups on the piano. Then, I found Band in a Box.
Then I tackled the progressions, the 1-4-5. I recall what a breakthrough for me it was when I realized I could find the 1-4-5 by simply raising the 3 from the chord a half step. Now, wouldn't you think that would have been obvious to a student?
No, for years, I counted out the rarely used progressions on my fingers.