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.

Whenever I get something stuck in the back of my throat, I dislodge it by drinking a beer.
It's called the Heineken Maneuver.

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software/hardware