Is the battery in the headlight?
White wire to alternator, attaches from the vreg. Is that unit in the headlight?
On the stock bike, battery, vreg., and alternator are far from headlight.
I'd have to assess your bike is wired by rank amature, and wouldn't trust much of it to be correct. Small wonder your bike doesn't charge the battery.
Methinks you'll need to make a wire diagram accurate to your bike.
You need:
Three yellow wires from alternator to rectifier need connecting. Rectifier green and red (minus and plus) need to connect to battery minus and plus respectively. This connects power from alternator output to battery input.
Next you need to control the alternator output strength. This is done with the voltage regulator. It needs power from the battery during run time, stock bikes provide this via the black wire ( switched battery POS) and green wire (battery NEG). The vreg then needs a green and white connection to the alternator, green is normally handled by frame and engine connections, ultimately connected to battery NEG terminal. The white wire is the control line from reg to alternator field. The reg sends power to the alternator, so the alternator can make power based on the battery voltage level. Battery low condition sends full battery power, battery full condition and the white wire voltage is throttled back, which reduces alternator output, in order to keep the battery from frying.
Clearly the wires colors only matter from an human I.D. Point of view. The internal copper inside the sleeve all looks the same to electrons, which are mostly color blind.
Your job is to ensure your bastardized bike wire connections conform to proper design function. You will also need to find the voltage regulator and rectifier components. The stock bike had these as separate units. "Modern" replacements may have combined these functions into one unit, with yet another color scheme for wire colors. You still need these functions if you want the alternator to charge the battery. Locate them on your bike or purchase one to make your bike distance rideable on the roadways limited only by your fuel supply.
Good luck!