Which side of this dipole is ground?

A dipole doesn’t have a ground plane like some other antennas. A dipole is a balanced antenna and both sides work off of each other equally.

With that said, this one is probably used for receiving and if one end is connected to the electrical ground (different thing from antenna ground plane) then it’s going to be the left side with the uninsulated wire most likely.

Neither side is ground. Due to electromagnetic field behavior, coax carries equal and opposite AC currents on the inner conductor and the inside surface of the shield; those equal and opposite currents drive the two dipole elements.

RF doesn’t penetrate shielded boxes and coax shields - so the outer surface and inner surface of the coax shield are seen as two different conductors at RF. In the pictured dipole, RF can flow out of the coax and back down the outside (and around the outside of the shielded receiver it’s connected to) because the open end of the coax “connects” them. So the coax shield is very much energized with (and receiving) RF; generally a ferrite bead choke is used to mitigate the unwanted shield currents.

With RF, “ground” doesn’t mean very much. There always has to be a circuit for current to flow; tying some point of the circuit to the chassis or to the power supply negative does not “zero it out” at all.

Looks like the left is the shielding on the cable so probably ground.